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

The Correct Option is D

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 $ .