# For any vector $\overrightarrow a\:\:and\:\:\overrightarrow b$ the angle between $|\overrightarrow a|\overrightarrow b+|\overrightarrow b|\overrightarrow a$ and $|\overrightarrow a|\overrightarrow b-|\overrightarrow b|\overrightarrow a$ is ?

$\begin{array}{1 1} 0 \\ \large\frac{\pi}{4} \\ \large\frac{\pi}{3} \\ \large\frac{\pi}{2} \end{array}$

## 1 Answer

Angle $\theta$ between $|\overrightarrow a|\overrightarrow b+|\overrightarrow b|\overrightarrow a$ and $|\overrightarrow a|\overrightarrow b-|\overrightarrow b|\overrightarrow a$ is
$cos\theta =\large\frac{(|\overrightarrow a|\overrightarrow b+|\overrightarrow b|\overrightarrow a).(|\overrightarrow a|\overrightarrow b-|\overrightarrow b|\overrightarrow a)}{|(|\overrightarrow a|\overrightarrow b+|\overrightarrow b|\overrightarrow a)|\:||\overrightarrow a|\overrightarrow b-|\overrightarrow b|\overrightarrow a|)}$
$=0$
$\therefore\:\theta=\large\frac{\pi}{2}$
answered Nov 29, 2013

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