Physics and Mathematics — Physics STD 12 Science — Question
Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsPhysics and Mathematics2 Marks
Question
Prove that $\vec{\text{A}}.(\vec{\text{A}}\times\vec{\text{B}})=0.$
✓
Answer
$\vec{\text{A}}.(\vec{\text{A}}\times\vec{\text{B}})=0$ (claim)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 $\vec{\text{A}}.(\vec{\text{A}}\times\vec{\text{B}})=0.$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.