Question

Give P = A + B and Q = A – B. If the magnitudes of vector P and Q are equal, what is the angle between vectors A and B ?

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

Answer 1

The correct option is C $\frac{\pi }{2}$

Let $\theta$ be the angle between A and B. Then magnitudes of vectors P and Q are given by
$P^2=A^2+B^2+2AB\cos \theta$
and $Q^2=A^2+B^2–2AB\cos \theta$
Since P = Q, it follows that $\cos \theta =0or\theta =\frac{\pi }{2}.$ Hence correct choice is (c).