If $|\vec{a}|=2,|\vec{b}|,=5$, and $\bar{a} . \bar{b}=0$, then $\bar{a} \times(\bar{a} \times(\bar{a} \times(\bar{a} \times(\bar{a} \times(\bar{a} \times \bar{b})))))$ is equal to
Answer & explanation
Correct answer: option 3
$\vec{a} \times(\vec{a} \times \vec{b})=(\vec{a} . \vec{b}) \vec{a}-(\vec{a} . \vec{a}) \vec{b}=-4 \vec{b}$
$\vec{a} \times(\vec{a} \times(-4 \vec{b}))=16 \vec{b}$ and process gives on
$=-320 \vec{b}$
Hence (3) is correct answer.