Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

Let $\overrightarrow{a} = 2\widehat{i}+\lambda _{1}\widehat{j}+3\widehat{k},\overrightarrow{b} = 4\widehat{i}+(3-\lambda _{2})\widehat{j}+6\widehat{k}$ and $\overrightarrow{c} = 3\widehat{i}+6\widehat{j}+(\lambda_{3}-1) \widehat{k},$ be three vectors such that $\vec{b}=2\vec{a}$

and $\vec{a}$ is perpendicular to $\vec{c}$ .Then a possible value of $(\lambda _{1},\lambda _{2},\lambda _{3})$ is:
Option 1)
(1,3,1)
Option 2)

(-1/2,4,0)
Option 3)

(1/2,4,-2)
Option 4)
(1,5,1)

Answers (1)

best_answer

Scalar multiplication -

fig 4

- wherein

The directed line segment becomes m times longer

Angle between vector a and vector b -

$\cos \Theta =\frac{\vec{a}.\vec{b}}{\left | \vec{a} \right |\left | \vec{b} \right |}$

- wherein

Here $0\leq \Theta \leq \pi$ ??????

From the concept

Given, $\vec{b}=2\vec{a}$

$4\hat{i}+(3-\lambda _{2})\hat{j}+6\hat{k}=4\hat{i}+2\lambda _{1}+6\hat{k}$

$=>3-\lambda _{2}=2\lambda _{1}$

$=>2\lambda _{1}+\lambda _{2}=3$ ................................(1)

Given $\vec{a}$ and $\vec{c}$ is perpendicular

So, $\vec{a}\cdot \vec{c}=0$

$=>6+6\lambda _{1}+3(\lambda _{3}-1)=0$

$=>2\lambda _{1}+\lambda _{3}=-1$ ...........................(2)

Now,

$(\lambda _{1},\lambda _{2},\lambda _{3})=(\lambda _{1},3-2\lambda _{1},-1-2\lambda _{1})$

$(\frac{-1}{2},4,0)$ satisfies this.

Option 1)

(1,3,1)

Option 2)

(-1/2,4,0)
Option 3)

(1/2,4,-2)

Option 4)

(1,5,1)

Posted by

admin

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

JEE Main 2026 application correction begins on jeemain.nta.nic.in; edit details by December 2

anam-khan

JEE Mains 2026 LIVE: NTA to conduct session 1 from January 21 to 30; exam pattern, syllabus

anam-khan

JEE Main 2026 correction window opens tomorrow; NTA allows exam city change

Latest Question