A plane mirror is moving with velocity ` -2 hati - 3 hatj + 4hatk `. A point object in front of the mirror move with a velocity `-3 hati + 4 hatj -4hatk `.
There ` hat j ` is along the normal to the plane mirror and facing towards the object. Find velocity of image.

Options

A. ` - 3 hati - 10 hatj - 4 hatk `
B. ` - 3 hatj + 11 hatj -4 hatk `
C. ` - 2 hatj + 11 hatj + 4hatk `
D. ` - 2 hatj - 10 hatj - 4 hatk `

Answer

A

Explanation

Given that
` vec ( V_ (MG) ) = - 2 hati - 3 hatj + 4hatk, vec (V_ (OG)) = - 3 hati + 4hatj - 4 hatk `
For the perpendicular (y) component :
` (V_(MG ) ) _ y = ((V_ (OG)) _ y + ( V_ (IG) ) _ y ) /( 2) rArr - 3 = (4 + (V_ (IG)) _ y) /( 2 ) = -10 `
And, other x and z component of velocity of image will remain the same as the velocity of the object w.r.t. ground, it does not depend on the velocity of mirror.
Means ` (V_(IG)) _ x = - 3 , ( V_ (IG)) _ z = (V_(OG)) _ z = - 4`. Then, ` vec (V_(IG)) = - 3 hati - 10 hatj - 4hatk`