Question

A plane mirror is moving with velocity `4hati + 5hatj + 8hatk`. A point object in front of the mirror moves with a velocity of `3hati + 4hatj + 5hatk`. Here `hatk` is along the normal to the plane mirror and facing toward the object. The velocity of the image is ______.

Options

• `-3hati - 4hatj + 5hatk`

• `3hati + 4hatj + 11hatk`

• `-3hati - 4hatj + 11hatk`

• `7hati + 9hatj + 11hatk`

Answer 1

A plane mirror is moving with velocity `4hati + 5hatj + 8hatk`. A point object in front of the mirror moves with a velocity of `3hati + 4hatj + 5hatk`. Here `hatk` is along the normal to the plane mirror and facing toward the object. The velocity of the image is `underlinebb(3hati + 4hatj + 11hatk)`.

Explanation:

`v_{OM(x)} = v_{IM(x)}`

⇒ 3 - 4 = `v_{I(x)} - 4`

⇒ v_I(x) = 3

`v_{OM(y)} = v_{IM(y)}`

⇒ 4 - 5 = `v_{I(y)} - 5`

⇒ v_I(y) = 4

`v_{OM(z)} = -v_{IM(z)}`

⇒ 5 - 8 = `-v_{I(z)} + 8`

⇒ `v_{IZ}` = 11

`v_1 = 3hati + 4hatj + 11hatk`