If $\vec a, \vec b, \vec c$ are non-coplanar vectors such that $\vec b×\vec c = \vec a, \vec c×\vec a = \vec b$ and $\vec a×\vec b = \vec c$, and $\vec a, \vec b, \vec c$ are unit vectors then $|\vec a+\vec b+\vec c|=$
Answer & explanation
Correct answer: option 4
We have,
$\vec a×\vec b = \vec c, \vec b×\vec c = \vec a$, and $\vec c×\vec a = \vec b$
$⇒\vec a⊥\vec b⊥\vec c$ and $|\vec a|=|\vec b|=|\vec c|=1$
$⇒|\vec a|^2+|\vec b|^2+|\vec c|^2=3$
$⇒|\vec a+\vec b+\vec c|^2=3$ $[∵ \vec a. \vec b=\vec b. \vec c = \vec c.\vec a=0]$
$⇒|\vec a+\vec b+\vec c|=\sqrt{3}$