If a, b and c are unit vectors such that a + b + c = 0, then angle between b and c is

Question

If $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ are unit vectors such that $\mathbf{a}+\mathbf{b}+\mathbf{c}=0$, then angle between $b$ and $c$ is

(a) $\frac{\pi}{3}$

(b) $\frac{2 \pi}{3}$

(c) $\frac{\pi}{6}$

(d) None of these

Answer 1

Since, $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ are unit vectors and $\mathbf{a}+\mathbf{b}+\mathbf{c}=\mathbf{0}$. It means they are along sides of an equilateral triangle.

$\theta=\pi-\frac{\pi}{3}=\frac{2 \pi}{3}$

So, The correct option of this question will be (B).