First slide

Vectors

Question

A vector perpendicular to both the vectors $2 \hat{i} - \hat{j} + 5 \hat{k}$ and X-axis is

Moderate

A

$\hat{j} + 5 \hat{j}$
B

$\hat{j} - 5 \hat{k}$
C

$5 \hat{j} + \hat{k}$
D

$\hat{i} + \hat{j} + \hat{k}$

Solution

Cross product of two perpendicular vector should be zero.
$|\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 2 & - 1 & 5 \\ 1 & 0 & 0 \end{matrix}| = - (0 - 5) \hat{j} + (1) \hat{k} = 5 \hat{j} + \hat{k}$
The vector perpendicular to both vectors is $5 \hat{j} + \hat{k}$

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