Question

If the angle between the vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is $\theta$ , the value of the product $(\overrightarrow{B}\times \overrightarrow{A}).\overrightarrow{A}$ is equal to:

• A. $B{A}^{2}cos\theta$
• B. $B{A}^{2}sin\theta$
• C. $B{A}^{2}sin\theta cos\theta$
• D. $0$

Answer 1

The correct option is D $0$

Since $\overrightarrow{B}\times \overrightarrow{A}$ will always be perpendicular to both $\overrightarrow{B}$ and $\overrightarrow{A}$. Thus, angle between $\overrightarrow{B}\times \overrightarrow{A}$ and $\overrightarrow{A}$ will be ${90}^0$.
Hence, $(\overrightarrow{B}\times \overrightarrow{A}).\overrightarrow{A}=0$