Physics and Mathematics — Physics STD 12 Science — Question

As, $\vec{\text{A}}\times\vec{\text{B}}=\text{AB}\sin\theta \ \hat{\text{n}}$

$\text{AB}\sin\theta \ \hat{\text{n}}$ is a vector which is perpendicular to the plane containing $\vec{\text{A}}$ and $\vec{\text{B}},$ this implies that it is also perpendicular to $\vec{\text{A}}.$ As dot product of two perpendicular vector is zero.

Thus $\vec{\text{A}}.(\vec{\text{A}}\times\vec{\text{B}})=0.$