First slide

Vectors

Question

A vector $P = 3 \hat{i} - 2 \hat{j} + a \hat{k}$ is perpendicular to the vector $Q = 2 \hat{i} + \hat{j} - \hat{k}$ . The value of a is

Moderate

A

2
B

1
C

4
D

3

Solution

Since, vector P is perpendicular to the vector Q.
$∴ P \cdot Q = 0 \Rightarrow (3 \hat{i} - 2 \hat{j} + a \hat{k}) \cdot (2 \hat{i} + \hat{j} - \hat{k}) = 0$
$\Rightarrow 6 - 2 - a = 0 \Rightarrow a = 4$

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