Question

The angle between two vectors `vec"a"` and `vec"b"` with magnitudes `sqrt(3)` and 4, respectively, and `vec"a" * vec"b" = 2sqrt(3)` is ______.

Options

• `pi/6`

• `pi/3`

• `pi/2`

• `(5pi)/2`

Answer 1

The angle between two vectors `vec"a"` and `vec"b"` with magnitudes `sqrt(3)` and 4, respectively, and `vec"a" * vec"b" = 2sqrt(3)` is `pi/3`.

Explanation:

Here, given that `|vec"a"| = sqrt(3)`

`|vec"b"|` = 4

And `vec"a" * vec"b" = 2sqrt(3)`

∴ From scalar product, we know that

`vec"a" * vec"b" = |vec"a"||vec"b"| cos theta`

⇒ `2sqrt(3) = sqrt(3) * 4 cos theta`

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

∴  `theta = pi/3`