Question

A vector of length $\ell$ is turned through the angle $\theta$ about its tail then the change in the position of vector's head is :-

• A. $\ell cos\frac{\theta }{2}$
• B. $2\ell sin\frac{\theta }{2}$
• C. $2\ell cos\frac{\theta }{2}$
• D. $\ell sin\frac{\theta }{2}$

Answer 1

The correct option is B $2\ell sin\frac{\theta }{2}$

$\Delta \ell =\sqrt{{\ell }_1^2+{\ell }_2^2-2{\ell }_1{\ell }_{2}cos\theta }$

$=\sqrt{{\ell }^2+{\ell }^2-2{\ell }^{2}cos\theta }=\ell \sqrt{2(1-cos\theta )}$

$=\ell \sqrt{2\times 2si{n}^2\frac{\theta }{2}}=2\ell sin\frac{\theta }{2}$