A plane mirror is moving with velocity $4 \hat{i} + 5 \hat{j} + 8 \hat{k}$ . A point object in front of the mirror moves with a velocity $3 \hat{i} + 4 \hat{j} + 5 \hat{k}$ . Here $\hat{k}$ is along the normal to the plane mirror and facing towards the object. The velocity of the image is :

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$- 3 \hat{i} - 4 \hat{j} + 11 \hat{k}$

$7 \hat{i} + 9 \hat{j} + 11 \hat{k}$

$- 3 \hat{i} - 4 \hat{j} + 5 \hat{k}$

$3 \hat{i} + 4 \hat{j} + 11 \hat{k}$

answer is B.

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Detailed Solution

Parallel to mirror, $υ_{I} = υ_{0} = 3 \hat{i} + 4 \hat{j}$
Perp to mirror, $υ_{I} = - υ_{0} + 2 υ_{M} = - (5 \hat{k}) + 2 (8 \hat{k}) = 11 \hat{k}$

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