If ${\bf{\vec a}},{\bf{\vec b}},{\bf{\vec c}}$ are the three vectors mutually perpendicular to each other to form a right handed system and $\left| {{\bf{\vec a}}} \right| = 1,{\rm{\;}}\left| {{\bf{\vec b}}} \right| = 3{\rm{\;and\;}}\left| {{\bf{\vec c}}} \right| = 5,{\rm{\;then\;}}\left[ {{\rm{\;}}{\bf{\vec a}} - 2{\bf{\vec b}}\;{\bf{\vec b}} - 3{\bf{\vec c}}\;{\bf{\vec c}} - 4{\bf{\vec a}}{\rm{\;}}} \right]$ is equal to

JEE MATHEMATICS MCQ: SCALAR TRIPLE PRODUCT

1 Easy

1 of 1

Application +4 | -1

\mathbf{\vec a},\mathbf{\vec b},\mathbf{\vec c}

are the three vectors mutually perpendicular to each other to form a right handed system and

\left| {\mathbf{\vec a}} \right| = 1,\mathrm{\;}\left| {\mathbf{\vec b}} \right| = 3\mathrm{\;and\;}\left| {\mathbf{\vec c}} \right| = 5,\mathrm{\;then\;}\left[ {\mathrm{\;}\mathbf{\vec a} - 2\mathbf{\vec b}\;\mathbf{\vec b} - 3\mathbf{\vec c}\;\mathbf{\vec c} - 4\mathbf{\vec a}\mathrm{\;}} \right]

is equal to

View answer and explanation

Correct option: D

 - 215

Option D (- 215) is correct because the scalar triple product is evaluated using the properties of mutually perpendicular vectors.