If $\overrightarrow{\mathrm{a}}$ and $\overrightarrow{\mathrm{b}}$ are perpendicular, then $\vec{a} \times(\vec{a} \times(\vec{a} \times(\vec{a} \times \vec{b})))$ is equal to
Correct Option: , 4
$\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}=0$
$\vec{a} \times(\vec{a} \times \vec{b})=(\vec{a} \cdot \vec{b}) \vec{a}-(\vec{a} \cdot \vec{a}) \vec{b}=-|\vec{a}|^{2} \vec{b}$
Now $\overrightarrow{\mathrm{a}} \times\left(\overrightarrow{\mathrm{a}} \times\left(-|\overrightarrow{\mathrm{a}}|^{2} \overrightarrow{\mathrm{b}}\right)\right)$
$=-|\vec{a}|^{2}(\vec{a} \times(\vec{a} \times \vec{b}))$
$=-|\vec{a}|^{2}\left(-|\vec{a}|^{2} \vec{b}\right)=|\vec{a}|^{4} \vec{b}$
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