Question

If `veca`  and  `vecb`  are two vectors such that `|vec{a}| = 1, |vec{b}| = 2 and vec{a}.vec{b} = root  3,` then the angle between `2vec{a} and vec{-b}` is ______.

Options

• `pi/6`

• `pi/3`

• `(5pi)/6`

• `(11pi)/6`

Answer 1

If `veca`  and  `vecb`  are two vectors such that `|vec{a}| = 1, |vec{b}| = 2 and vec{a}*vec{b} = root  3,` then the angle between `2vec{a} and vec{-b} " is " underlinebb((11pi)/6)`.

Explanation:

`|veca| = 1  vec{a} * vec{b} = root  3`

`|vecb| = 2`

`veca*vecb = |veca| |vecb| cos θ`

`sqrt3` = 2 cos θ

cos θ = `root  3/2  θ =pi/6`

`(2veca).(-vecb) = 2 |veca| |vecb| cos θ`

θ `= 2pi - pi/6`

θ `= (11pi)/6`