JEE MAIN - Physics (2022 - 25th June Morning Shift - No. 3)
Which of the following relations is true for two unit vector $$\widehat A$$ and $$\widehat B$$ making an angle $$\theta$$ to each other?
$$|\widehat A + \widehat B| = |\widehat A - \widehat B|\tan {\theta \over 2}$$
$$|\widehat A - \widehat B| = |\widehat A + \widehat B|\tan {\theta \over 2}$$
$$|\widehat A + \widehat B| = |\widehat A - \widehat B|cos{\theta \over 2}$$
$$|\widehat A - \widehat B| = |\widehat A + \widehat B|\cos {\theta \over 2}$$
คำอธิบาย
$$\because$$ $$\left| {\widehat A - \widehat B} \right| = 2\sin \left( {{\theta \over 2}} \right)$$
and, $$\left| {\widehat A + \widehat B} \right| = 2\cos \left( {{\theta \over 2}} \right)$$
$$ \Rightarrow {{\left| {\widehat A - \widehat B} \right|} \over {\left| {\widehat A + \widehat B} \right|}} = \tan \left( {{\theta \over 2}} \right)$$