A plane mirror is moving with velocity $4 \hat{i} + 5 \hat{j} + 8 \hat{k} .$ The point object in front of the mirror moves with a velocity $3 \hat{i} + 4 \hat{j} + 5 \hat{k}, h e r e \hat{k}$ is along the normal to the plane mirror and facing towards the object. The velocity of the images with respect to ground (The given velocities are w.r.t ground) is :

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

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

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

$7 \hat{i} + 4 \hat{j} + 11 \hat{k}$

answer is B.

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Detailed Solution

${\vec{v}}_{M} = 4 \hat{i} + 5 \hat{j} + 8 \hat{k}, {\vec{v}}_{0} = 3 \hat{i} + 4 \hat{j} + 5 \hat{k}$

$∴$ Plane of the mirror is xy $∴ {\vec{v}}_{_{I}} = 3 \hat{i} + 4 \hat{j}$ and for $\hat{k} v_{I Z} = 2 {\vec{v}}_{_{M Z}} - {\vec{v}}_{_{O Z}} = 2 \times 8 - 5 = 11 \Rightarrow {\vec{v}}_{I} = 3 \hat{i} + 4 \hat{j} + 11 \hat{k}$

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