Question

If $|\mathbf{a}| = 3,|\mathbf{b}| = 4,|\mathbf{c}| = 5$ and $\mathbf{a} + \mathbf{b} + \mathbf{c} = 0,$ then the angle between a and b is

• A. 0
• B. $\frac{\pi}{6}$
• C. $\frac{\pi}{3}$
• D. $\frac{\pi}{2}$

Answer 1

Answer: (D)

$\frac{\pi}{2}$

Answer 2

$\mathbf{a} + \mathbf{b} = - \mathbf{c} \Rightarrow |\mathbf{a}|^{2} + |\mathbf{b}|^{2} + 2|\mathbf{a}||\mathbf{b}|\cos\theta = |\mathbf{c}|^{2}$

$\Rightarrow \cos\theta = 0 \Rightarrow \theta = \frac{\pi}{2}.$