Question

If `vecα = hati - 4hatj + 9hatk and vecβ = 2hati - 8hatj + λhatk` are two mutually parallel vectors, then λ is equal to ______.

Options

• −18

• 18

• `(−34)/9`

• `34/9`

Answer 1

If `vecα = hati - 4hatj + 9hatk and vecβ = 2hati - 8hatj + λhatk` are two mutually parallel vectors, then λ is equal to 18.

Explanation:

`vecα = hati - 4hatj + 9hatk`

`vecβ = 2hati - 8hatj + λhatk`

are mutually parallel values

`vecα = µvecβ`

`vecβ = 2hati - 8hatj + λhatk`

= `2(hati - 4hatj + λ/2 hatk)`

`vecβ = 2vecα    (∵ vecα || vecβ)`

`∴ λ/2 = 9`

λ = 18