Question

A vector of length l is turned through the angle q about its tail. The change in the position vector of its head is -

• A. lcosq/2
• B. 2l sin (q/2)
• C. 2lcosq/2
• D. l sin (q/2)

Answer 1

Answer: (B)

2l sin (q/2)

Answer 2

Given that |$\left| \overset{\rightarrow}{r_{1}} \right| = \left| \overset{\rightarrow}{r_{2}} \right|$ = l

$\overset{\rightarrow}{\Delta r} = \overset{\rightarrow}{r_{2}} - \overset{\rightarrow}{r_{1}}$ $\left| \overset{\rightarrow}{\Delta r} \right| = \sqrt{r_{2}^{2} + r_{1}^{2} - 2r_{1}r_{2}\cos\theta}$ = 2 l

sin (q/2)