Question

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

• A. B $A^2 \sin \theta$
• B. B $A^2 \cos \theta$
• C. B $A^2 \sin \theta \cos \theta$
• D. zero

Answer 1

Answer: (D)

zero

Answer 2

Let $\overrightarrow{A} \times \overrightarrow{B} = \overrightarrow{C}$
The cross product of $\overrightarrow{B}$ and $\overrightarrow{A}$ is perpendicular to the plane containing $\overrightarrow{A}$ and $\overrightarrow{B}$

i, e perpendicular to $\overrightarrow{A}$. If a dot product of this cross product and $\overrightarrow{A}$ is taken, as the cross product is perpendicular to $\overrightarrow{A}$ , $\overrightarrow{C} \times \overrightarrow{A} = 0$.
Therefore product of $( \overrightarrow{B} \times \overrightarrow{A} ) \cdot \overrightarrow{A} = 0$ .