Question

Let `veca = hati - 2hatj + 3hatk`. If `vecb` is a vector such that `veca.vecb = |vecb|^2` and `|veca - vecb| = sqrt(7)` then `|vecb|` equals

Options

• 7

• 14

• `sqrt(7)`

• 21

Answer 1

`bb(sqrt(7))`

Explanation:

`|veca - vecb| = sqrt(7)`

On squaring both sides,

`|veca - vecb|^2 = (sqrt(7))^2`

`|veca|^2 + |vecb|^2 - 2veca.vecb = 7`

Given, `veca = hati - 2hatj + 3hatk`

`|veca| = sqrt((1)^2 + (-2)^2 + (3)^2`

`|veca| = sqrt(14)`

`|veca|^2 = 14`

`14 + |vecb|^2 - 2veca.vecb = 7`

`14 + |vecb|^2 - 2|vecb|^2 = 7`   ...`["Given", veca.vecb = |vecb|^2]`

`14 - |vecb|^2 = 7`

`|vecb|^2 = 7`

`|vecb| = sqrt(7)`