Question

A vector of magnitude a is rotated through an angle q. What is the magnitude of the change in the vector?

• A. (a) 2asin $\frac{\theta}{2}$
• A. (b) 2a cos$\frac{\theta}{2}$
• A. (c) 2a sin q
• A. (d) 2acosq

Answer 1

(a)

$|\overset{\rightarrow}{a_{1}}| = |\overset{\rightarrow}{a_{2}}| = a$

$|\Delta\overset{\rightarrow}{a}| = |\overset{\rightarrow}{a_{2}}–\overset{\rightarrow}{a_{1}}|$

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

= $\sqrt{a^{2} + a^{2} - 2a^{2}\cos\theta}$

= 2a sin q/2