Question

Assertion: $\overrightarrow{A}\times \overrightarrow{B}$ is perpendicular to both $\overrightarrow{A}+\overrightarrow{B}$ as well as $\overrightarrow{A}-\overrightarrow{B}.$
Reason: $\overrightarrow{A}+\overrightarrow{B}$ as well as $\overrightarrow{A}-\overrightarrow{B}$ lie in the plane containing $\overrightarrow{A}$ and $\overrightarrow{B}$ but $\overrightarrow{A}\times \overrightarrow{B}$ lies perpendicular to the plane containing $\overrightarrow{A}$ and $\overrightarrow{B}.$

• 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 A If both assertion and reason are true and the reason is the correct explanation of the assertion.

Cross product of two vectors is perpendicular to the plane containing both the vectors.