Question

Let $u$ and $v$ be two nonzero vectors, if $|u +v|=|u-v|$ then

• A. u and v have the same direction
• B. u and v are perpendicular
• C. u and v have the opposite direction
• D. Data Insufficient

Answer 1

Answer: (B)

$|u+ v|=|u-v|$
Squaring on both sides,
$|u+ v|^{2}=|u-v|^{2}$
$|u|^{2}+|v|^{2}+2 \bar{u} v=|u|^{2}+|v|^{2}+2(\bar{u} v)$
$4 \bar{u}, \bar{v})=0$
$\bar{u} \cdot v=0$
$\bar{u} \perp \bar{v}$