Question

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

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

Answer 1

The correct option is D BA${}^2$sin $\theta$ cos $\theta$

According to question,

$(\overrightarrow{A}\times \overrightarrow{B}).\overrightarrow{A}=\left(ABsin\theta \right).\overrightarrow{A}$

$(\overrightarrow{A}\times \overrightarrow{B}).\overrightarrow{A}=B{A}^{2}sin\theta cos\theta$

where, $\theta =$ angle between the vector $\overrightarrow{A}$ and $\overrightarrow{B}$

The correct option is D.