Given that $\overrightarrow A + \overrightarrow B = \overrightarrow C $and that $\overrightarrow C $ is $ \bot $ to $\overrightarrow A $. Further if $|\overrightarrow A |\, = \,|\overrightarrow C |,$then what is the angle between $\overrightarrow A $ and $\overrightarrow B $
Given that $\overrightarrow A + \overrightarrow B = \overrightarrow C $and that $\overrightarrow C $ is $ \bot $ to $\overrightarrow A $. Further if $|\overrightarrow A |\, = \,|\overrightarrow C |,$then what is the angle between $\overrightarrow A $ and $\overrightarrow B $
$\frac{\pi }{4}radian$
$\frac{\pi }{2}radian$
$\frac{{3\pi }}{4}radian$
$\pi \,\,radian$
Given that $\overrightarrow A + \overrightarrow B = \overrightarrow C $and that $\overrightarrow C $ is $ \bot $ to $\overrightarrow A $. Further if $|\overrightarrow A |\, = \,|\overrightarrow C |,$then what is the angle between $\overrightarrow A $ and $\overrightarrow B $
Given, $A+B=C$
and $B=C-A$
Since, $C \perp A$, therefore
$B^{2}=C^{2}+A^{2}$
Also, $|C|=|A|,$ therefore
$B^{2}=2 A^{2} \Rightarrow B=\sqrt{2} A$
$\mathrm{Now}, A^{2}+B^{2}+2 A B \cos \theta=C^{2}=A^{2}$
$\therefore \cos \theta=\frac{1}{\sqrt{2}}$
This gives $\theta=\frac{3 \pi}{4}$ rad