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ISRO | ISRO CS 2017 | Question 10

Last Updated : 22 Mar, 2018

If vectors $\vec{a}=2\hat{i}+\lambda \hat{j}+\hat{k }$ and $\vec{b}=\hat{i}-2 \hat{j}+3\hat{k }$ are perpendicular to each other, then value of λ is

(A) 2/5
(B) 2
(C) 3
(D) 5/2

Answer: (D)

Explanation: Given, vectors $\vec{a}=2\hat{i}+\lambda \hat{j}+\hat{k }$ and $\vec{b}=\hat{i}-2 \hat{j}+3\hat{k }$ are perpendicular to each other, so $\vec{a} \dot \vec{b} = 0$

$\vec{a} \dot \vec{b} = 2\times 1 - 2\times \lambda + 3\times 1 = 0$

$2\times 1 - 2\times \lambda + 3\times 1 = 0$

$-2\lambda = -5$

$\lambda = 5 / 2$

So, option (D) is correct.

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