Q. Let $\overrightarrow{\mathbf{v}} = 2\widehat{\mathbf{i}} + \widehat{\mathbf{j}} - \widehat{\mathbf{k}}\ and\ \overrightarrow{\mathbf{w}} = \widehat{\mathbf{i}} + 3\widehat{\mathbf{k}},\ If\ \overrightarrow{\mathbf{u}}$ is a unit vector, then maximum value of the scalar triple product $\lbrack\ \overrightarrow{\mathbf{u}}\mathbf{\ }\overrightarrow{\mathbf{v}}\mathbf{\ }\overrightarrow{\mathbf{w}}\ \rbrack$ is
Explanation
(c)
$\left\lbrack \ \overrightarrow{\mathbf{u}}\mathbf{\ }\overrightarrow{\mathbf{v}}\mathbf{\ }\overrightarrow{\mathbf{w}}\ \right\rbrack = \left| \overrightarrow{\mathbf{u}}\mathbf{\bullet}\left( \mathbf{\ }\overrightarrow{\mathbf{v}}\mathbf{\ \times}\overrightarrow{\mathbf{w}} \right) \right|$
$= \left| \overrightarrow{\mathbf{u}} \bullet \left( 3\widehat{\mathbf{i}} - 7\widehat{\mathbf{j}} - \widehat{\mathbf{k}}\ \right) \right|$
$= \left| \ \overrightarrow{\mathbf{u}}\ \right|\sqrt{59}\cos\theta$
$\therefore$ Maximum value of $\left\lbrack \ \overrightarrow{\mathbf{u}}\mathbf{\ }\overrightarrow{\mathbf{v}}\mathbf{\ }\overrightarrow{\mathbf{w}}\ \right\rbrack = \sqrt{59}\ \ \ (\because\left| \overrightarrow{\mathbf{u}} \right| = 1,\cos{\theta\ \leq 1)}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.