Question

Two vector $\overrightarrow{A}$ and $\overrightarrow{B}$ have equal magnitudes. Then the vector $\overrightarrow{A}+\overrightarrow{B}$ is perpendicular to

• A. $A\times B$
• B. $3A-3B$
• C. All of these
• D. $A-B$

Answer 1

The correct option is A $A\times B$

$\overrightarrow{A}+\overrightarrow{B}$ lies in the plane containing $\overrightarrow{A}$ and $\overrightarrow{B}$.

But $\overrightarrow{A}\times \overrightarrow{B}$ is a vector perpendicular to both $\overrightarrow{A}$ and $\overrightarrow{B}$.

Hence, $\overrightarrow{A}\times \overrightarrow{B}$ perpendicular to $\overrightarrow{A}+\overrightarrow{B}$.

Final answer (a)