Question

For any two vectors A and B, if $A\cdot B =|A \times B |$ , the magnitude of C = A + B is equal to

• A. $\sqrt{A^2 + B^2}$
• B. $A + B$
• C. $\sqrt{A^2 + B^2 + \frac{AB}{\sqrt2}}$
• D. $\sqrt{A^2 + B^2 + \sqrt2 \, AB}$

Answer 1

Answer: (D)

$AB \cos \, \theta = AB \sin \theta \Rightarrow tan \, \theta = 1 \Rightarrow \theta = 45^\circ$
$\therefore |C| = \sqrt{A^2 + B^2 + 2 AB \cos \, 45^\circ} $
$= \sqrt{A^2 + B^2 + \sqrt2 \, AB}$