Question

If the sum of two unit vectors is also a unit vector, then the magnitude of their difference is -

• A. (a)$\sqrt{2}$
• A. (b)$\sqrt{3}$
• A. (c)$\sqrt{5}$
• A. (d)$\sqrt{7}$

Answer 1

(b)

For sum

$|\bar{R}|$=$\sqrt{P^{2} + Q^{2} + 2PQ\cos\theta}$

1 = $\sqrt{1^{2} + 1^{2} + 2 \times 1 \times 1 \times \cos\theta}$

q = 120⁰

For difference

$|\bar{R}|$=$\sqrt{P^{2} + Q^{2} - 2PQ\cos\theta}$

=$\sqrt{1^{2} + 1^{2} - 2\cos 120º}$=$\sqrt{3}$