Kinematics Question 257

Question: The angle between the vectors $ \overrightarrow{A} $ and $ \overrightarrow{B} $ is $ \theta . $ The value of the triple product $ \overrightarrow{A}.(\overrightarrow{B}\times \overrightarrow{A}) $ it’s [CBSE PMT 1991, 2005]

Options:

A) $ A^{2}B $

B) Zero

C) $ A^{2}B\sin \theta $

D) $ A^{2}B\cos \theta $

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Answer:

Correct Answer: B

Solution:

Let $ \overrightarrow{A}.(\overrightarrow{B}\times \overrightarrow{A})=\overrightarrow{A}.\overrightarrow{C} $

Here $ \overrightarrow{C}=\overrightarrow{B}\times \overrightarrow{A} $ Which is perpendicular to both vector $ \overrightarrow{A} $

and $ \overrightarrow{B} $ \ $ \overrightarrow{A}.\overrightarrow{C}=0 $



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