A particle is moving with velocity ($\hat{i}+2\hat{j}+3\hat{k})m/s$. A plane mirror exists in the x - y plane. The mirror has a velocity $(\hat{i}+2\hat{j})m/s$. Velocity of the image (in $m/s$) is:

The correct option is B $\hat{i}+2\hat{j}-3\hat{k}$
Since the mirror is in x-y plane, only the z-component of the velocity of the image with respect to the mirror will be reversed as compared to the velocity of the object with respect to the mirror
Hence
velocity of the object with respect to the mirror
${\overrightarrow{v}}_{om}={\overrightarrow{v}}_o-{\overrightarrow{v}}_m=(\hat{i}+2\hat{j}+3\hat{k})-(\hat{i}+2\hat{j})$
${\overrightarrow{v}}_{om}=3\hat{k}$
Hence velocity of the image with respect to the mirror
${\overrightarrow{v}}_{im}=-3\hat{k}$
${\overrightarrow{v}}_i={\overrightarrow{v}}_m-3\hat{k}$
${\overrightarrow{v}}_i=\hat{i}+2\hat{j}-3\hat{k}$