Question

The angle between the vectors $\overset{\rightarrow}{A}$ and $\overset{\rightarrow}{B}$ is $\theta.$ The value of the triple product $\overset{\rightarrow}{A}.(\overset{\rightarrow}{B} \times \overset{\rightarrow}{A})$ 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 $\overset{\rightarrow}{A}.(\overset{\rightarrow}{B} \times \overset{\rightarrow}{A}) = \overset{\rightarrow}{A}.\overset{\rightarrow}{C}$

Here $\overset{\rightarrow}{C} = \overset{\rightarrow}{B} \times \overset{\rightarrow}{A}$ is perpendicular to both vector

$\overset{\rightarrow}{A}$ and $\overset{\rightarrow}{B}$ ∴ $\overset{\rightarrow}{A}.\overset{\rightarrow}{C} = 0$