A vector perpendicular to both the vectors 2i^-j^+5k^ and X-axis is

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

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

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

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

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

answer is C.

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Detailed 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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