Question

What is the angle between two vectors `veca` and `vecb` with magnitudes `sqrt(3)` and 2 respectively, such that `veca * vecb = sqrt(6)`

Options

• `pi/2`

• `pi/4`

• `pi/6`

• `pi/8`

Answer 1

`pi/4`

Explanation:

We know that the angle 0 between two vectors `vec` and `vecb` is given by

`cos theta = (veca * vecb)/(|veca||vecb|)`

⇒ `cos theta = sqrt(6)/((sqrt(3))(2)) = ((sqrt(3))(sqrt(2)))/((sqrt(3))(sqrt(2))) = 1/sqrt(2) = cos  pi/4`

∴ `theta = pi/4`.