Given that A + B = C and that C is perpendicular to A. Further, if |A| = |C|, then what is the angle between A and B?

From the figure, B cos $\theta$ = C                           …(i)
and B sin $\theta$  = A                                               …(ii)

Given, IAI = I CI
$\therefore$IB cos $\theta$| = IB sin $\theta$| or $\theta$ = 45⁰
Hence, angle between A and B is 135⁰ or  $\frac{3\pi }{4}$