Question

Assertion: If dot product and cross product of $\overrightarrow{A}$ and $\overrightarrow{B}$ are zero, it implies that one of the vector $\overrightarrow{A}$ and $\overrightarrow{B}$ must be null vector.
Reason: Null vector is a vector with zero magnitude.

• A. If both assertion and reason are true and the reason is the correct explanation of the assertion.
• B. If both assertion and reason are true but reason is not the correct explanation of the assertion.
• C. If assertion is true but reason is false.
• D. If the assertion and reason both are false.
• E. If assertion is false but reason is true.

Answer 1

The correct option is B If both assertion and reason are true but reason is not the correct explanation of the assertion.

$\overrightarrow{A}.\overrightarrow{B}=|\overrightarrow{A}||\overrightarrow{B}|\cos \theta =0$
$\overrightarrow{A}\times \overrightarrow{B}=|\overrightarrow{A}||\overrightarrow{B}|\sin \theta =0$

If $\overrightarrow{A}$ and $\overrightarrow{B}$ are not null vectors, then both $\sin \theta$ and $\cos \theta$ cannot be zero simultaneously, so it is essential that one of the vector must be null vector.