First slide

Vectors

Question

If the vectors $\vec{A} = (a \hat{i} - a \hat{j} + \hat{k}) a n d \vec{B} = (a \hat{i} + \hat{j} - 2)$ are mutually perpendicular, then positive value of ‘a’ is

Easy

A

2
B

4
C

3
D

1

Solution

(1)
$\begin{array}{l} \vec{A} . \vec{B} = 0 \\ \Rightarrow (a \hat{i} - a \hat{j} + \hat{k}) . (a \hat{i} + \hat{j} - 2) = 0 \\ \Rightarrow a^{2} - a - 2 = 0 \Rightarrow (a - 2) (a + 1) = 0 \Rightarrow a = 2, - 1 \end{array}$

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