Question

If the vector `vecb` is collinear with the vector `veca = (2sqrt(2), -1, 4)` and `|vecb|` = 10, then ______.

Options

• `veca ± vecb = vec0`

• `veca ± 2vecb = vec0`

• `2veca ± vecb = vec0`

• `veca ± 3vecb = vec0`

Answer 1

If the vector `vecb` is collinear with the vector `veca = (2sqrt(2), -1, 4)` and `|vecb|` = 10, then `underlinebb(2veca ± vecb = vec0)`.

Explanation:

`vecb = λ(2sqrt(2)hati - hatj + 4hatk)`

`|vecb| = |λ| sqrt(8 + 1 + 16)`

10 = 5|λ|

⇒ λ = ±2

`vecb = ±2veca`

⇒ `2veca ± vecb` = 0