Question

The vector `vecp` perpendicular to the vectors `veca = 2hati + 3hatj - hatk` and `vecb = hati - 2hatj + 3hatk` and satisfying the condition `vecp.(2hati - hatj + hatk)` = –6 is ______.

Options

• `-hati + hatj + hatk`

• `3(-hati + hatj + hatk)`

• `2(-hati + hatj + hatk)`

• `hati - hatj + hatk`

Answer 1

The vector `vecp` perpendicular to the vectors `veca = 2hati + 3hatj - hatk` and `vecb = hati - 2hatj + 3hatk` and satisfying the condition `vecp.(2hati - hatj + hatk)` = –6 is `underlinebb(3(-hati + hatj + hatk))`.

Explanation:

`veca xx vecb = |(hati, hatj, hatk),(2, 3, -1),(1, -2, 3)|`

`veca xx vecb = hati(9 - 2) - hatj(6 + 1) + hatk(-4 - 3)`

= `7(hati - hatj - hatk)`

`vecp = λ(hati - hatj - hatk)`

`vecp.(2hati - hatj + hatk) = λ(hati - hatj - hatk).(2hati - hatj + hatk)`

= –6

λ(2 + 1 – 1) = –6

⇒ λ = –3

So `vecp = -3(hati - hatj - hatk)`

`vecp = 3(-hati + hatj + hatk)`