A plane mirror is moving with velocity `4 (hat i) + 4 (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

Options

A. `-3hati -4hatj + 5hatk`
B. `3hati +4hatj + 11hatk`
C. `-3hati -4hatj + 11hatk`
D. `7hati +4hatj + 11hatk`

Answer

B

Explanation

`vecV_(M) = 4hati + 5 hatj + 8hatk , vecV_(0) = 3hati + 4hatj + 5hatk`
`because` Plane of the mirror is xy
`therefore vecV_(I)= 3hati+4hatj` and for `veckv_(12)`
=`2V_(MZ) - V_(OZ) = 2xx8 -5=11`
`implies vecV_(I) = 3hati +4hatj + 11hatk`