If $\vec a·\vec b=\vec a·\vec c, \vec a×\vec b=\vec a×\vec c$ and $\vec a \ne 0$, then the vector $\vec b$ in equal to.

$\vec c$

The correct answer is Option (2) → $\vec c$

Given:

$\vec{a}\cdot\vec{b} = \vec{a}\cdot\vec{c}$ and $\vec{a}\times\vec{b} = \vec{a}\times\vec{c}$

If $\vec{a} \ne \vec{0}$:

Then both dot and cross product equalities imply $\vec{b} = \vec{c}$.