Question

The angle between the vectors $\vec { A }$ and $\vec { A } \cdot ( \vec { B } \times \vec { A } )$ is

• A. $A ^ { 2 } B$
• B. Zero
• C. $A ^ { 2 } B \sin \theta$
• D. $A ^ { 2 } B \cos \theta$

Answer 1

Answer: (B)

Zero

Answer 2

Let $\vec { A } \cdot ( \vec { B } \times \vec { A } ) = \vec { A } \cdot \vec { C }$

Here $\vec { C } = \vec { B } \times \vec { A }$ Which is perpendicular to both vector $\vec { A }$ and $\vec { B }$ ∴ $\vec { A } \cdot \vec { C } = 0$