Question

If the vectors `overlinea = 2hati - qhatj + 3hatk` and `overlineb = 4hati - 5hatj + 6hatk` are collinear, then the value of q is ______

Options

• 5 

• `1/2`

• 2

• `5/2`

Answer 1

If the vectors `overlinea = 2hati - qhatj + 3hatk` and `overlineb = 4hati - 5hatj + 6hatk` are collinear, then the value of q is `underline(5/2)`.

Explanation:

Since the vectors are collinear,

`overlineb = lambdaoverlinea`

⇒ `(4hati - 5hatj + 6hatk) = lambda(2hati - qhatj + 3hatk)`

On comparing, we get

2λ = 4 and λq = 5

⇒ λ = 2 and 2q = 5

⇒ q = `5/2`