Question

A vector perpendicular to the line `vecr=hati+hatj-hatk+λ(3hati-hatj)` is ______.

Options

• `5hati+hatj+6k`

• `hati+3hatj+5hatk`

• `2hati-2hatj`

• `9hati-3hatj`

Answer 1

A vector perpendicular to the line `vecr=hati + hatj - hatk + λ(3hati - hatj) " is " underlinebb(hati + 3hatj + 5hatk)`.

Explanation:

`vecr=hati+hatj-hatk+x(3hati-hatj+0hatk)`

a₁ = 3, b₁ = −1, c₁ = 0

On checking options one by one taking option (B) as a₂ = 1, b₂ = 3, c₂ = 5

We know that, vector perpendicular to line, only when 

a₁a₂ + b₁b₂ + c₁c₂ = 0

= (3)(1) + (−1)(3) + (0)(5)

= 3 − 3 + 0

= 0