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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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