Vector addition and Vector Subtraction – JEE Main Study Material

Question

Which of the following quantities is not a vector quantity?

A.	Velocity
B.	Current density
C.	Current
D.	Force

Question

The resultant of two forces 3P and 2P is R. If the first force is doubled, then the resultant is also doubled. The angle between the forces in degrees is

A.	120
B.	60
C.	180
D.	90

Question

The ratio of maximum and minimum magnitudes of the resultant of two vectors $|\vec{a}|$ and $|\vec{b}|$ is $3: 1$, Now $|\vec{a}|=$

A.	$\|\vec{b}\|$
B.	$2\|\vec{b}\|$
C.	$3\|\vec{b}\|$
D.	$4\|\vec{b}\|$

Question

Asked in: JEE Main 2019-2019

Two vectors $\vec{A}\: and\: \vec{B}$ have equal magnitudes. The magnitudes of $\left ( \vec{A}\: +\: \vec{B} \right )$ is 'n' times the magnitudes of $\left ( \vec{A}\: - \: \vec{B} \right )$ . The angle between $\vec{A}\: and\: \vec{B}$ is :

A.	$\sin ^{-1}\left [ \frac{n-1}{n+1} \right ]$
B.	$\cos ^{-1}\left [ \frac{n^{2}-1}{n^{2}+1} \right ]$
C.	$\sin ^{-1}\left [ \frac{n^{2}-1}{n^{2}+1} \right ]$
D.	$\cos ^{-1}\left [ \frac{n-1}{n+1} \right ]$

Question

The magnitude and direction of the resultant of two vectors $\vec{A}$ and $\vec{B}$ in terms of their magnitudes and angle $\theta$ between them is

A.	$R=\sqrt{A^2+B^2-2 A B \cos \theta}, \tan \alpha=\frac{B \sin \theta}{A+B \cos \theta}$
B.	$R=\sqrt{A^2+B^2+2 A B \cos \theta}, \tan \alpha=\frac{B \cos \theta}{A+B \sin \theta}$
C.	$R=\sqrt{A^2+B^2-2 A B \cos \theta}, \tan \alpha=\frac{A \sin \theta}{B+A \sin \theta}$
D.	$R=\sqrt{A^2+B^2+2 A B \cos \theta}, \tan \alpha=\frac{B \sin \theta}{A+B \cos \theta}$

Question

Two forces are such that the sum of their magnitude is 18N, and their resultant is 12N which is perpendicular to the smaller force. Then the magnitude of the forces are

A.	12N, 6N
B.	13N, 5N
C.	10N, 8N
D.	16N, 2N

Question

Asked in: JEE Main 2019-2019

Two forces P and Q, of magnitude 2 F and 3 F, respectively, are at an angle $\theta$ with each other. If the force Q is doubled, then their resultant also gets doubled. Then the angle $\theta$ (in degrees) is :

A.	30
B.	60
C.	90
D.	120

Question

Asked in: JEE Main 2020-2020

The sum of two forces $\vec{P}$ and $\vec{Q}$ is $\vec{R}$ such that $\left | \vec{R} \right |=\left | \vec{P} \right |.$ The angle $\theta$ (in degrees) that the resultant of $2\vec{P}$ and $\vec{Q}$ will make with $\vec{Q}$ is ,

A.	90
B.	120
C.	45
D.	30

Question

Asked in: JEE Main 2021-2021

In an octagon ABCDEFGH of equal side, what is the sum of $\overrightarrow{A B}+\overrightarrow{A C}+\overrightarrow{A D}+\overrightarrow{A E}+\overrightarrow{A F}+\overrightarrow{A G}+\overrightarrow{A H}$ if $\overrightarrow{A O}=2 \widehat{i}+3 \widehat{j}-4 \widehat{k}$

A.	$16 \widehat{i}+24 \widehat{j}-32 \widehat{k}$
B.	$16 \widehat{i}+24 \widehat{j}+32 \widehat{k}$
C.	$-16 \widehat{i}-24 \widehat{j}+32 \widehat{k}$
D.	$16 \widehat{i}-24 \widehat{j}+32 \widehat{k}$

Question

A particle is moving along north after moving for 2 sec with a speed of 4 m/s, its speed becomes 5m/s. Its displacement (in meters) at end of 7 sec is ?

A.	33
B.	43
C.	38
D.	31

Question

Asked in: JEE Main 2022-2022

Which of the following relations is true for two unit vector $\hat{\mathrm{A}}$ and $\hat{\mathrm{B}}$ making an angle $\theta$ to each other ?

A.	$\|\hat{\mathrm{A}}+\hat{\mathrm{B}}\|=\|\hat{\mathrm{A}}-\hat{\mathrm{B}}\| \tan \theta / 2$
B.	$\|\hat{\mathrm{A}}-\hat{\mathrm{B}}\|=\|\hat{\mathrm{A}}+\hat{\mathrm{B}}\| \tan \theta / 2$
C.	$\|\hat{\mathrm{A}}+\hat{\mathrm{B}}\|=\|\hat{\mathrm{A}}-\hat{\mathrm{B}}\| \cos \theta / 2$
D.	$\|\hat{\mathrm{A}}-\hat{\mathrm{B}}\|=\|\hat{\mathrm{A}}+\hat{\mathrm{B}}\| \cos \theta / 2$

Question

Asked in: JEE Main 2022-2022

Two vectors $\vec{A}\: and\: \vec{B}$ have equal magnitudes. If the magnitude of $\vec{A}\: +\: \vec{B}$ is equal to two times the magnitude of $\vec{A}\: -\: \vec{B}$ , then the angle between $\vec{A}$ and $\vec{B}$ will be :

A.	$\sin ^{-1}\left(\frac{3}{5}\right)$
B.	$\sin ^{-1}\left(\frac{1}{3}\right)$
C.	$\cos ^{-1}\left(\frac{3}{5}\right)$
D.	$\cos ^{-1}\left(\frac{1}{3}\right)$

Question

Asked in: JEE Main 2022-2022

If $\vec{A}=(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-\hat{\mathrm{k}}) \mathrm{m}$ and $\vec{B}=(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}) \mathrm{m}$. The magnitude of the component of vector $\vec{A}$ along vector $\vec{B}$ will be---- $\qquad$ m.

A.	2
B.	-
C.	-
D.	-

Question

Asked in: JEE Main 2021-2021

If $\vec{A}$ and $\vec{B}$ are two vectors satisfying the relation $\overrightarrow{\mathrm{A}} \cdot \overrightarrow{\mathrm{B}}=|\overrightarrow{\mathrm{A}} \times \overrightarrow{\mathrm{B}}|$. Then the value of $|\vec{A}-\vec{B}|_{\text {will be : }}$

A.	$\sqrt{A^2+B^2}$
B.	$\sqrt{A^2+B^2+\sqrt{2} A B}$
C.	$\sqrt{A^2+B^2+2 A B}$
D.	$\sqrt{A^2+B^2-\sqrt{2} A B}$

Question

Asked in: JEE Main 2021-2021

Two vectors $\overrightarrow{\mathrm{P}}$ and $\overrightarrow{\mathrm{Q}}$ have equal magnitudes. If the magnitude of $\overrightarrow{\mathrm{P}}+\overrightarrow{\mathrm{Q}}$ is $n$ times the magnitude of $\overrightarrow{\mathrm{P}}-\overrightarrow{\mathrm{Q}}$ , then angle between $\overrightarrow{\mathrm{P}}$ and $\overrightarrow{\mathrm{Q}}$ is :

A.	$\sin ^{-1}\left(\frac{n-1}{n+1}\right)$
B.	$\cos ^{-1}\left(\frac{\mathrm{n}-1}{\mathrm{n}+1}\right)$
C.	$\sin ^{-1}\left(\frac{\mathrm{n}^{2}-1}{\mathrm{n}^{2}+1}\right)$
D.	$\cos ^{-1}\left(\frac{\mathrm{n}^{2}-1}{\mathrm{n}^{2}+1}\right)$

Question

Asked in: JEE Main 2021-2021

Match List I with List II, and Choose the correct answer from the options given below :

A.	(a) $\rightarrow$ (iv), (b) $\rightarrow$ (i), (c) $\rightarrow$ (iii), (d) $\rightarrow$ (ii)
B.	(a) $\rightarrow$ (iv), (b) $\rightarrow$ (iii), (c) $\rightarrow$ (i), (d) $\rightarrow$ (ii)
C.	$(\mathrm{a}) \rightarrow$ (iii), (b) $\rightarrow$ (ii), (c) $\rightarrow$ (iv), (d) $\rightarrow($ i)
D.	$(\mathrm{a}) \rightarrow$ (i), (b) $\rightarrow$ (iv), (c) $\rightarrow$ (ii), (d) $\rightarrow$ (iii)

Question

Asked in: JEE Main 2021-2021

Two vectors $\overrightarrow{\mathrm{X}}$ and $\overrightarrow{\mathrm{Y}}$ have equal magnitude. The magnitude of $(\overrightarrow{\mathrm{X}}-\overrightarrow{\mathrm{Y}})$ is $n$ times the magnitude of $(\overrightarrow{\mathrm{X}}+\overrightarrow{\mathrm{Y}})$ . The angle between $\overrightarrow{\mathrm{X}}$ and $\overrightarrow{\mathrm{Y}}$ is :

A.	$\cos ^{-1}\left(\frac{-n^{2}-1}{n^{2}-1}\right)$
B.	$\cos ^{-1}\left(\frac{n^{2}-1}{-n^{2}-1}\right)$ -
C.	$\cos ^{-1}\left(\frac{n^{2}+1}{-n^{2}-1}\right)$
D.	$\cos ^{-1}\left(\frac{n^{2}+1}{n^{2}-1}\right)$

Question

Asked in: JEE Main 2021-2021

Assertion A : If A, B, C, D are four points on a semi-circular arc with centre at 'O' such that

$
\begin{aligned}
& |\overrightarrow{\mathrm{AB}}|=|\overrightarrow{\mathrm{BC}}|=|\overrightarrow{\mathrm{CD}}| \text {, then } \\
& \overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{AC}}+\overrightarrow{\mathrm{AD}}=4 \overrightarrow{\mathrm{AO}}+\overrightarrow{\mathrm{OB}}+\overrightarrow{\mathrm{OC}}
\end{aligned}
$

Reason R : Polygon law of vector addition yields

$
\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{BC}}+\overrightarrow{\mathrm{CD}}+\overrightarrow{\mathrm{AD}}=2 \overrightarrow{\mathrm{AO}} \overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{BC}}+\overrightarrow{\mathrm{CD}}+\overrightarrow{\mathrm{AD}}=2 \overrightarrow{\mathrm{AO}}
$

In the light of the above statements, choose the most appropriate answer from the options given below:

A.	A is correct but R is not correct.
B.	A is not correct but R is correct.
C.	Both A and R are correct and R is the correct explanation of A.
D.	Both A and R are correct but R is not the correct explanation of A.

Question

Asked in: JEE Main 2021-2021

The magnitude of vectors $\overrightarrow{O A}, \overrightarrow{O B}$ and $\overrightarrow{O C}$ in the given figure are equal. the direction of $\overrightarrow{O A}+\overrightarrow{O B}-\overrightarrow{O C}$ with x-axis will be:

A.	$\tan ^{-1} \frac{(\sqrt{3}-1+\sqrt{2})}{(1+\sqrt{3}-\sqrt{2})}$
B.	$\tan ^{-1} \frac{(1-\sqrt{3}-\sqrt{2})}{(1+\sqrt{3}+\sqrt{2})}$
C.	$\tan ^{-1} \frac{(\sqrt{3}-1+\sqrt{2})}{(1-\sqrt{3}+\sqrt{2})}$
D.	$\tan ^{-1} \frac{(1+\sqrt{3}-\sqrt{2})}{(1-\sqrt{3}-\sqrt{2})}$

Question

Asked in: JEE Main 2021-2021

$\text { The angle between vector }(\vec{A}) \text { and }(\vec{A}-\vec{B}) \text { is: }$

A.	$\tan ^{-1}\left(\frac{B \cos \theta}{A-B \sin \theta}\right)$
B.	$\tan ^{-1}\left(\frac{\sqrt{3} B}{2 A-B}\right)$
C.	$\tan ^{-1}\left(\frac{-\frac{B}{2}}{A-B \frac{\sqrt{3}}{2}}\right)$
D.	$\tan ^{-1}\left(\frac{A}{0 \cdot 7 B}\right)$

Question

Asked in: JEE Main 2021-2021

Statement I:
Two forces $(\vec{P}+\vec{Q})$ and $(\vec{P}-\vec{Q})_{\text {where }} \vec{P} \perp \vec{Q}$, when act at an angle $\theta_1$ to each other, the magnitude of their resultant is $\sqrt{3\left(\mathrm{P}^2+\mathrm{Q}^2\right)}$, when they act at an angle $\theta_2$, the magnitude of their resultant becomes $\sqrt{2\left(\mathrm{P}^2+\mathrm{Q}^2\right)}$. This is possible only when $\theta_1<\theta_2$.
Statement II :
In the situation given above.

$
\theta_1=60^{\circ} \text { and } \theta_2=90^{\circ}
$
In the light of the above statements, choose the most appropriate answer from the options given below:

A.	Statement I is false but Statement II is true.
B.	Both Statement I and Statement II are false.
C.	Both Statement I and Statement II are true.
D.	Statement I is true but Statement II is false.

Question

The ratio of maximum and minimum magnitudes of the resultant of two vectors $\vec{a}$ and $\vec{b}$ is $3: 1$, Now $|\vec{a}|=$

A.	$\|\vec{b}\|$
B.	$2\|\vec{b}\|$
C.	$3\|\vec{b}\|$
D.	$4\|\vec{b}\|$

Question

Which of the following is correct?

A.	$\vec{A}+(\vec{B}+\vec{C})=(\vec{A}+\vec{B})+\vec{C}$
B.	$\vec{A}\times\vec{B}=\vec{B}\times\vec{A}$
C.	$\vec{A}\times(\vec{B}\times\vec{C})=\vec{B}\times(\vec{A}\times\vec{C})$
D.	None of the above

Question

Asked in: JEE Main 2006-2006

A particle has two velocities of equal magnitude inclined to each other at an angle θ. If one of them is halved, the angle between the other and the original resultant velocity is bisected by the new resultant. Then $\theta$ is :

A.	$90^{\circ}$
B.	$120^{\circ}$
C.	$45^{\circ}$
D.	$60^{\circ}$

Question

Asked in: BITSAT-2018

Two forces are such that the sum of their magnitudes is 18 N and their resultant is 12 N which is perpendicular to the smaller force. Then the magnitudes of the forces are

A.	12 N, 6 N
B.	13 N, 5 N
C.	10 N, 8 N
D.	16 N, 2 N

Question

If $|\vec{A}+\vec{B}|=|\vec{A}|=|\vec{B}|$, then the angle between $\vec{A}$ and $\vec{B}$ is (in degrees):

A.	120
B.	60
C.	90
D.	0

Question

Asked in: JEE Main 2019-2019

In the cube of side 'a' shown in the figure, the vector from the central point of the face ABOD to the central point of the face BEFO will be:

A.	$\frac{1}{2} a(\widehat{k}-\widehat{i})$
B.	$\frac{1}{2} a(\widehat{i}-\widehat{k})$
C.	$\frac{1}{2} a(\widehat{j}-\widehat{i})$
D.	$\frac{1}{2} a(\widehat{j}-\widehat{k})$

Question

If $\vec{A}=5 \hat{i}+10 \hat{j}$ and $\vec{B}=10 \hat{i}+5 \hat{j}$, then the magnitude of $\vec{A}+\vec{B}$ is $x\sqrt{2}$. Find x.

A.	15
B.	10
C.	5
D.	20

Question

If $\vec{A}=5 \hat{i}+10 \hat{j}$ and $\vec{B}=10 \hat{i}+5 \hat{j}$, then the magnitude of $\vec{A}-\vec{B}$ is x$\sqrt{2}$. Find x.

A.	5
B.	10
C.	15
D.	20

Question

If $\overrightarrow{P}+\overrightarrow{Q}=\overrightarrow{R}\: and\: \left | \overrightarrow{P} \right |=8,\left | \overrightarrow{Q} \right |=15\: and\: \left | \overrightarrow{R} \right |=17$ . What is the angle (in degrees) between $\overrightarrow{P}\: and\: \overrightarrow{Q}$ ?

A.	90
B.	180
C.	0
D.	60

Question

Asked in: JEE Main 2019-2019

The output of the given logic circuit is :

A.	$A \bar{B}+\bar{A} B$
B.	$ A \bar{B} $
C.	$A B+\overline{A B}$
D.	$\bar{A} B$

Question

Asked in: JEE Main 2019-2019

To get output '1' at R, for the given logic gate circuit, the input values must be:

A.	X=0, Y=1
B.	X=1, Y=1
C.	X=1, Y=0
D.	X=0, Y=0

Question

Asked in: JEE Main 2019-2019

The logic gate equivalent to the given logic circuit is :

A.	NAND
B.	OR
C.	NOR
D.	AND

Question

Two vectors $\vec{A}$ and $\vec{B}$ inclined at an angle $\theta$ have a resultant $\vec{R}\$ which makes an angle $\alpha$ with $\vec{A}$ . If the direction of $\vec{A}$ and $\vec{B}$ are interchanged, the resultant will have the same:

A.	Direction
B.	Magnitude
C.	Direction as well as magnitude
D.	None of these

Question

Which of the following quantities is dependent on the choice of orientation of the coordinate axes?

A.	$\vec{A}+\vec{B}$
B.	${{A}_{x}}+{{B}_{y}}$
C.	$\left\| \vec{A}+\vec{B} \right\|$
D.	Angle between $\vec{A} \And \vec{B}$

Question

Vectors $\vec{A}\And \vec{B}$ include an angle $\theta$ between them. If $\vec{A}+\vec{B}$ and $\vec{A}-\vec{B}$ respectively subtend angles $\alpha \And \beta$ with $\vec{A}$ , then $(\tan \alpha +\tan \beta )$ is:

A.	$\frac{AB\sin \theta }{{{A}^{2}}+{{B}^{2}}{{\cos }^{2}}\theta }$
B.	$\frac{2AB\sin \theta }{{{A}^{2}}-{{B}^{2}}{{\cos }^{2}}\theta }$
C.	$\frac{{{A}^{2}}{{\sin }^{2}}\theta }{{{A}^{2}}+{{B}^{2}}{{\cos }^{2}}\theta }$
D.	$\frac{{{B}^{2}}{{\sin }^{2}}\theta }{{{A}^{2}}-{{B}^{2}}{{\cos }^{2}}\theta }$

Question

Which of the following is not a property of the null vector

A.	$\vec{A}+\vec{0}=\vec{A}$
B.	$\lambda \vec{0}=\vec{0}$ where $\lambda$ is a scalar
C.	$\vec{A}-\vec{A}=\vec{0}$
D.	$0\vec{A}=\vec{A}$

Question

Given $\vec{A}+\vec{B}+\vec{C}+\vec{D}=0$ which of the following statements is not correct?

A.	$\vec{A},\vec{B},\vec{C}\And \vec{D}$ must be a null vector
B.	The magnitude $(\vec{A}+\vec{C})$ is equal to the magnitude of $(\vec{B}+\vec{D})$
C.	The magnitude $(\vec{A}+\vec{C})$ is equal to the magnitude $(\vec{B}+\vec{D})$
D.	None of these

Question

$\left| \vec{A}+\vec{B} \right|=\left| \vec{A}-\vec{B} \right|$ then the angle between $\vec{A}\And \vec{B}$ will be :

A.	${{30}^{\circ }}$
B.	${{45}^{\circ }}$
C.	${{60}^{\circ }}$
D.	${{90}^{\circ }}$

Question

Two vectors are given by $\vec{A}=(3\hat{i}+\hat{j}+3\hat{k})\And \vec{B}=(3\hat{i}+5\hat{j}-2\hat{k})$ . Find the third vector $\vec{C}$ if $\vec{A}+3\vec{B}-\vec{C}=0\$ .

A.	$12\hat{i}+14\hat{j}+12\hat{k}$
B.	$13\hat{i}+17\hat{j}+12\hat{k}$
C.	$12\hat{i}+16\hat{j}-3\hat{k}$
D.	$15\hat{i}+13\hat{j}+4\hat{k}$

Question

The components of the sum of vectors $2\hat{i}+3\hat{j}\And 2\hat{j}+3\hat{k}$ along x and y respectively are :

A.	2 and 5
B.	4 and 6
C.	2 and 6
D.	4 and 3

Question

Asked in: BITSAT-2018

A vector $\vec{A}$ is rotated by small angle $\Delta \Theta$ radians $(\Delta \Theta<<1)$ to get a new vector $\vec{B}$.In that case $|\vec{B}-\vec{A}|$ is :

A.	$0$
B.	$\|\vec{A}\|\left(1-\frac{\Delta \Theta^2}{2}\right)$
C.	$\|\vec{A}\| \Delta \Theta$
D.	2

Question

The sum of the magnitudes of two forces acting at the point is 16N. If the resultant force is 8N and its direction is perpendicular to the smaller force, then the forces are,

A.	6N and 10N
B.	8N and 8N
C.	4N and 12N
D.	2N and 14N

Question

Asked in: JEE Main-2023

Two forces having magnitude $A$ and $\frac{A}{2}$ are perpendicular to each other. The magnitude of their resultant is:

A.	$\frac{5 \mathrm{~A}}{2$
B.	$\frac{\sqrt{5} \mathrm{~A}^2}{2}$
C.	$\frac{\sqrt{5} \mathrm{~A}}{4}$
D.	$\frac{\sqrt{5} \mathrm{~A}}{2}$

Question

Asked in: JEE Main-2023

When a vector $\vec{A}=2 \hat{i}+3 \hat{j}+2 \hat{k}$ is subtracted from a vector $\vec{B}$ , it gives a vector equal to $2 \hat{j}$ . Then the magnitude of the vector $\vec{B}$ will be:

A.	$\sqrt{33}$
B.	$\sqrt{5}$
C.	$\sqrt{13}$
D.	$\sqrt{6}$

Question

Asked in: JEE Main-2024

If two vectors $\vec{A}$ and $\vec{B}$ having equal magnitude R inclined at an angle $\theta$, then

A.	$\|\overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}}\|=2 \mathrm{R} \cos \left(\frac{\theta}{2}\right)$
B.	$\|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}\|=2 \mathrm{R} \cos \left(\frac{\theta}{2}\right)$
C.	$\|\overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}}\|=\sqrt{2} \mathrm{R} \sin \left(\frac{\theta}{2}\right)$
D.	$\|\vec{A}+\vec{B}\|=2 R \sin \left(\frac{\theta}{2}\right)$

Question

A car travelling due north at 20 m/s turns west and travels at the same speed. The change in its velocity

A.	40 m/s N-W
B.	$20 \sqrt{2} m / s N-W$
C.	40 m/s S -W
D.	$20 \sqrt{2} \mathrm{~m} / \mathrm{s} S-W$

Question

If a vector is multiplied by a real number (-3) then

A.	Its magnitude will become three times
B.	Its direction will be same as before
C.	its magnitude will be unchanged
D.	Both A and B

Question

If $\vec{P}=3 \hat{i}+4 \hat{j}+7 \hat{k}$ and $\vec{Q}=\hat{i}+2 \hat{j}+\hat{k}$ the value of magnitude of resolution of $\vec{P}-\vec{Q}$ is.

A.	$\sqrt{45}$
B.	$2 \sqrt{11}$
C.	$4 \sqrt{11}$
D.	$5 \sqrt{11}$

Question

If $\vec{A}$ and $\vec{B}$ are non zero vectors. Which obey the relation $|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$ then the angle between them is -

A.	$0^{\circ}$
B.	$90^{\circ}$
C.	$120^{\circ}$
D.	$40^{\circ}$

Question

If $\vec{P}+\vec{Q}=\vec{R}_{\text {and }}|\vec{P}|=8,|\vec{Q}|=15$ and $|\vec{R}|=17$ what is the angle between $\vec{P}$ and $\vec{Q}_{\text {is }}$

A.	$\pi$
B.	$\frac{\pi}{2}$
C.	0
D.	none of these

Question

If $\vec{P}+\vec{Q}+\vec{R}$ and $|\vec{P}|=8|\vec{Q}|=215$ and $|\vec{R}|=17$ what is the angle between $\vec{P}$ and $\vec{Q}$

A.	$\pi$
B.	$\frac{\pi}{2}$
C.	$0^{\circ}$
D.	none of above

Question

The position of a particle in a 500 triangular coordinate system is (4,6,-2). Its position vector will be

A.	$4 \hat{i}-6 \hat{j}+2 k$
B.	$-4 \hat{i}+6 \hat{j}+2 \hat{k}$
C.	$4 \hat{i}+6 \hat{j}-2 \hat{k}$
D.	$4 \hat{i}-6 \hat{j}-2 \hat{k}$

Question

The position of a particle in a rectangular co-ordinate system is (4,6,-2). Then its position vector is :

A.	$4 \widehat{i}+6 \widehat{j}-2 \hat{k}$
B.	$4 \widehat{i}-6 \widehat{j}-2 \hat{k}$
C.	$-4 \widehat{i}+6 \widehat{j}+2 \widehat{k}$
D.	$4 \widehat{i}+6 \widehat{j}+2 \widehat{k}$

Question

Two forces of 12 N and 8 N act upon a body. The resultant force on the body has a maximum value of

A.	0 N
B.	8 N
C.	4N
D.	20 N

Question

Which of the following is true for the addition of the vectors?

A.	$\vec{A}+\vec{B}=\vec{B}+\vec{A}$
B.	$(\vec{A}+\vec{B})+\vec{C} \neq \vec{A}(\vec{B}+\vec{C})$
C.	$\vec{A}+\vec{B}=\|\vec{A}\|+\|\vec{B}\|$
D.	Both A and B

Question

which of the following is true for the addition of vector

A.	$\vec{A}+\vec{B}=\vec{B}+\vec{A}$
B.	$(\vec{A}+\vec{B})+\vec{C} \neq \vec{A}+(\vec{B}+\vec{C})$
C.	$\vec{A}+\vec{B}=\|\vec{B}\|+\|\vec{A}\|$
D.	Both A and B

Question

Which of the following statements is true

1) The angle between negative vectors is equal to 180 degree

2) The magnitude of negative vectors is equal

3 ) negative vectors always have the same initial point

A.	1 and 2
B.	2 and 3
C.	only 1
D.	1 and 3

Question

Asked in: BITSAT-2018

A vector perpendicular to $(4 \hat{i}-3 \hat{j})$ may be:

A.	$(4 \hat{i}+3 \hat{j})$
B.	$7 \hat{k}$
C.	$6 \hat{i}$
D.	$(3 \hat{i}-4 \hat{j})$

Question

Asked in: BITSAT-2018

The minimum number of vectors of equal magnitude required to produce a zero resultant is:-

A.	2
B.	3
C.	4
D.	more than 4

Question

Asked in: BITSAT-2018

The resultant of $\vec{A}$ and $\vec{B}$ makes an angle $\alpha$ with $\vec{A}$ and $\beta$ with $\vec{B}$, then :-

A.	$\alpha \propto \beta$
B.	$\alpha<\beta$ if $A>B$
C.	$\alpha<\beta$ if $A=B$
D.	$\alpha<\beta$ if $A=B$

Question

Three vectors $A, B$ and $C$ add up to zero. Find which is false.
(a) $(A * B)^* C$ is not zero unless $B, C$ are parallel
(b) (A*B).C is not zero unless B,C are parallel
(c) If $A, B, C$ define a plane, $(A * B)^{\star} C$ is in that plane
(d) $\left(A^* B\right) \cdot C=|A||B||C| \rightarrow C^2=A^2+B^2$

A.	a,c
B.	a,d
C.	b,d
D.	a,d

Question

For two vectors A and $\mathrm{B},|A+B|=|A-B|$ is always true when
(a) $|A|=|B| \neq 0$
(b) $|A| \perp|B|$
(c) $|A|=|B| \neq 0$ and A and B are parallel or anti parallel
(d) when either $|A|$ or $|B|$ is zero.

A.	(a) and (b) only
B.	(b) and (d) only
C.	(c) and (d) only
D.	(a) and (c) only

Question

Asked in: JEE Main-2024

Three vectors $\mathrm{\overrightarrow{O P}, \overrightarrow{O Q}}$ and $\mathrm{\overrightarrow{O R}}$ each of magnitude A are acting as shown in figure. The resultant of the three vectors is $\mathrm{A \sqrt{x}}$. The value of x is ________.

A.	3
B.	13
C.	2
D.	12

Question

Asked in: JEE Main-2024

Two forces $\vec{F}_1$ and $\vec{F}_2$ are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between $\overrightarrow{\mathrm{F}}_1$ and $\vec{F}_2$ is $\cos ^{-1}\left(\frac{1}{n}\right)$. The value of $|n|$ is:

A.	6
B.	12
C.	15
D.	20

Question

Asked in: KVPY SB/SX-2009

The five sides of a regular pentagon are represented by vectors $\overrightarrow{A_1}, \overrightarrow{A_2}, \overrightarrow{A_3}, \overrightarrow{A_4}$, and $\overrightarrow{A_5}$ in cyclic order as shown. Corresponding vertices are represented $\overrightarrow{B_1}, \overrightarrow{B_2}, \overrightarrow{B_3}, \overrightarrow{B_4}$, and $\overrightarrow{B_5}$, drawn from the centre of the pentagon.

Then,

$
\overrightarrow{B_2}+\overrightarrow{B_3}+\vec{B}_4+\overrightarrow{B_5}=
$

A.	$\overrightarrow{A_1}$
B.	$-\overrightarrow{A_1}$
C.	$\overrightarrow{B_1}$
D.	$-\overrightarrow{B_1}$

Question

If $\vec{A}=4 \hat{i}-3 \hat{j}$ and $\vec{B}=6 \hat{i}+8 \hat{j}$ then magnitude and direction of $\vec{A}+\vec{B}$ will be

A.	$5, \tan ^{-1}(3 / 4)$
B.	$3 \sqrt{5}, \tan ^{-1}(1 / 2)$
C.	$10, \tan ^{-1}(5)$
D.	$25, \tan ^{-1}(3 / 4)$

Question

If $\vec{A}$ and $\vec{B}$ are non-zero vector which obey the relation $|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$, then the angle between them is -------- $^{\circ}$

A.	90
B.	0
C.	60
D.	120

Question

Two lines with direction cosines ${ }_{\mathrm{}} l_1, m_1, n_1$ and $l_2, m_2, n_2$ are at right angles if

A.	$l_1 l_2+m_1 m_2+n_1 n_2=0$
B.	$l_1=l_2, m_1=m_2, n_1=n_2$
C.	$l_1 l_2=m_1 m_2=n_1 n_2$
D.	None of these

Exam	Chapter
JEE MAIN	Kinematics

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