Question

$|\overrightarrow{a}+\overrightarrow{b}{|}^2+|\overrightarrow{a}-\overrightarrow{b}{|}^2$ is equal to 2($|\overrightarrow{a}{|}^2$ - $|\overrightarrow{b}{|}^2$).
If true enter 1 else enter 0

Answer 1

$|\overrightarrow{a}+\overrightarrow{b}{|}^2=(\overrightarrow{a}+\overrightarrow{b}).(\overrightarrow{a}+\overrightarrow{b})=|\overrightarrow{a}{|}^2+2|\overrightarrow{a}||\overrightarrow{b}|cos\left(\theta \right)+|\overrightarrow{b}{|}^2$ ....1

$|\overrightarrow{a}-\overrightarrow{b}{|}^2=(\overrightarrow{a}-\overrightarrow{b}).(\overrightarrow{a}-\overrightarrow{b})=|\overrightarrow{a}{|}^2-2|\overrightarrow{a}||\overrightarrow{b}|cos\left(\theta \right)+|\overrightarrow{b}{|}^2$ .....2

Adding equations 1 and 2, $\Rightarrow |\overrightarrow{a}+\overrightarrow{b}{|}^2+|\overrightarrow{a}-\overrightarrow{b}{|}^2=2(|\overrightarrow{a}{|}^2+|\overrightarrow{b}{|}^2)$,

$\therefore$ Ans =0