Q. If $\overrightarrow{\mathbf{a}},\ \overrightarrow{\mathbf{b}},\ \overrightarrow{\mathbf{c}}$ are non-coplanar and $\left\lbrack \overrightarrow{\mathbf{a}} + \ \overrightarrow{\mathbf{b}}\ \overrightarrow{\mathbf{b}} + \overrightarrow{\mathbf{c}}\ \ \overrightarrow{\mathbf{c}} + \overrightarrow{\mathbf{a}} \right\rbrack = k\left\lbrack \overrightarrow{\mathbf{a}}\ \overrightarrow{\mathbf{b}}\ \overrightarrow{\mathbf{c}} \right\rbrack,$ then $k$ is equal to
A) 0
B) 1
C) 2
D) 3
Explanation
(c)
By the properties of scalar triple product
$\left\lbrack \overrightarrow{\mathbf{a}} + \overrightarrow{\mathbf{b}}\ \overrightarrow{\mathbf{b}} + \overrightarrow{\mathbf{c}}\ \overrightarrow{\mathbf{c}} + \overrightarrow{\mathbf{a}} \right\rbrack = 2\left\lbrack \overrightarrow{\mathbf{a}}\ \overrightarrow{\mathbf{b}}\ \overrightarrow{\mathbf{c}} \right\rbrack$
$\therefore k = 2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.