Question

Let `veca, vecb` and `vecc` be three unit vectors such that `veca xx (vecb xx vecc) = sqrt(3)/2 (vecb + vecc)`. If `vecb` is not parallel to `vecc`, then the angle between `veca` and `vecc` is

Options

• 0

• `2pi`

• `(5pi)/6`

• `pi/6`

Answer 1

`pi/6`

Explanation:

Given `|veca| = |vecb| = |vecc|` = 1 and `veca xx (vecb xx vecc) = sqrt(3)/2 (vecb + vecc)`

⇒ `(veca.vecc)vecb - (veca * vecb)vecc = sqrt(3)/2 vecb + sqrt(3)/2 vecc`

on comapring, we get `veca.vecc = sqrt(3)/2`

⇒ `|veca||vecc| cos theta = sqrt(3)/2`

⇒ `cos theta = cos  pi/6` 

⇒ `theta = pi/6`