Q. If $\overrightarrow{\mathbf{a}},\overrightarrow{\mathbf{b}}$ are any two vwctors, then $\left( 2\overrightarrow{\mathbf{a}} + 3\overrightarrow{\mathbf{b}} \right) \times \left( 5\overrightarrow{\mathbf{a}} + 7\overrightarrow{\mathbf{b}} \right) + \overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}}$ is equal to
A) $\overrightarrow{\mathbf{0}}$
B) 0
C) $\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}}$
D) $\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{a}}$
Explanation
(a)
$\left( 2\overrightarrow{\mathbf{a}} + 3\overrightarrow{\mathbf{b}} \right) \times \left( 5\overrightarrow{\mathbf{a}} + 7\overrightarrow{\mathbf{b}} \right) + \overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}}$
$= \overrightarrow{\mathbf{0}} + 14\left( \overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}} \right) - 15\left( \overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}} \right) + \overrightarrow{\mathbf{0}} + \overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}}$
$= \overrightarrow{\mathbf{0}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.