Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

Let $\vec{u}=\hat{i}+\hat{j},\; \; \vec{v}=\hat{i}-\hat{j}\; and\; \vec{w}=\hat{i}+2\hat{j}+3\hat{k}.$ If $\hat{n}$ is a unit vector such that $\vec{u}\cdot \hat{n}=0$ and $\vec{v}\cdot \hat{n}=0,$ then $\left |\vec{w}\cdot \vec{n} \right |$ is equal to

Option 1)
1

Option 2)
2

Option 3)
3

Option 4)
0

Answers (1)

best_answer

As we learnt in

Vector Product of two vectors(cross product) -

If $\vec{a}$ and $\vec{b}$ are two vectors and $\Theta$ is the angle between them , then $\vec{a}\times \vec{b}=\left |\vec{a} \left | \right |\vec{b} \right |Sin\Theta \hat{n}$

- wherein

$\hat{n}$ is unit vector perpendicular to both $\vec{a} \: and \: \vec{b}$

Scalar Product of two vectors (dot product) -

$\vec{a}\vec{b}=\left | a \right |\left | b \right |Cos\theta$

- wherein

$\Theta$ is the angle between the vectors $\vec{a}\: and\:\vec{b}$

Since $\vec{n}$ is perpendicular to $\vec{u} \ and \ \vec{v}$ $\vec{u} \times \vec{v} =\begin{vmatrix} \hat i & \hat j & \hat k\\ 1 & 1 & 0 \\ 1 & -1 & 0 \end{vmatrix} = -2 \hat k$

Unit vector of $\vec{u} \times \vec{v} =\hat{k}$

Now, $\begin{vmatrix} \hat w. \hat n \end{vmatrix} =3$

Option 1)

1

This option is incorrect.

Option 2)

2

This option is incorrect.

Option 3)

3

This option is correct.

Option 4)

0

This option is incorrect.

Posted by

Plabita

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

BTech Admission 2025 Live: JEE Mains, SRMJEEE, MET registrations underway; MHT CET syllabus updates

anam-khan

Centre issues coaching guidelines, prohibits centres from using false claims like '100% selection'

anam-khan

BTech Admissions 2025 Live: JEE Mains, SRMJEE, VITEEE dates out; AEEE, MET registrations underway

Latest Question