Question

If `bara` and `barb` are unit vectors, then the angle between `bara` and `barb` for `(sqrt(3)bara - barb)` be a unit vector, is ______.

Options

• 90°

• 60°

• 45°

• 30°

Answer 1

If `bara` and `barb` are unit vectors, then the angle between `bara` and `barb` for `(sqrt(3)bara - barb)` be a unit vector, is 30°.

Explanation:

`|sqrt(3)bara - barb|` = 1

∴ `|sqrt(3)bara - barb|^2` = 1

∴ `(sqrt(3)bara - barb)*(sqrt(3)bara - barb)` = 1

∴ `3a^2 - 2sqrt(3)bara*barb + b^2` = 1

∴ 3 + 1 = `1 + 2sqrt(3)bara*barb`

∴ `bara*barb = 3/(2sqrt(3)) = sqrt(3)/2`

∴ ab cos θ = `sqrt(3)/2`

∴ cos θ = `sqrt(3)/2`   ...(∵ `bara` and `barb` are unit vectors)

∴ θ = 30°