Question

If $A+B=C$ and that $C$ is perpendicular to $A$. What is the angle between $A$ and $B$, if $\left|A\right|=\left|C\right|$?

• A. $\frac{\pi }{4}rad$
• B. $\frac{\pi }{2}rad$
• C. $\frac{3\pi }{4}rad$
• D. $\pi rad$

Answer 1

Answer: (C)

$\frac{3\pi }{4}rad$

Given, $A+B=C$
and $B=C-A$
Since, $C\perp A$, therefore
$B^2=C^2+A^2$
Also, $\left|C\right|=\left|A\right|$, therefore
$B^2=2A^2\Rightarrow B=\sqrt{2}A$
Now, $A^2+B^2+2AB\cos \theta =C^2=A^2$
$\therefore \cos \theta =\frac{1}{\sqrt{2}}$
This gives $\theta =\frac{3\pi }{4}rad$