If ${\bf{\vec a}}{\rm{\;and\;}}{\bf{\vec b}}$ are two non-zero, non-collinear vectors, then $2\,\,\left[ {{\bf{\vec a}}\;\;{\bf{\vec b}}\;\,\widehat {{\bf{\dot i}}}} \right]\widehat {\,{\bf{\dot i}}} + 2\left[ {{\bf{\vec a}}\;\;{\bf{\vec b}}\;\,\widehat {{\bf{\dot j}}}} \right]\widehat {\,{\bf{\dot j}}} + 2\,\,\left[ {{\bf{\vec a}}\;\;{\bf{\vec b}}\;\,{\bf{\hat k}}} \right]\,\,{\bf{\hat k}} + \left[ {{\bf{\vec a}}\;\;{\bf{\vec b}}\,\;{\bf{\vec a}}\;} \right]$ is equal to

$2\left( {{\bf{\vec a}}\,\; \times \,{\bf{\vec b}}} \right)\;$

${\bf{\vec a}}\;\, \times \,\,{\bf{\vec b}}\;$

${\bf{\vec a}} + {\bf{\vec b}}\;$

JEE MATHEMATICS MCQ: SCALAR TRIPLE PRODUCT

1 Easy

1 of 1

Application +4 | -1

\mathbf{\vec a}\mathrm{\;and\;}\mathbf{\vec b}

are two non-zero, non-collinear vectors, then

2\,\,\left[ {\mathbf{\vec a}\;\;\mathbf{\vec b}\;\,\widehat {\mathbf{\dot i}}} \right]\widehat {\,\mathbf{\dot i}} + 2\left[ {\mathbf{\vec a}\;\;\mathbf{\vec b}\;\,\widehat {\mathbf{\dot j}}} \right]\widehat {\,\mathbf{\dot j}} + 2\,\,\left[ {\mathbf{\vec a}\;\;\mathbf{\vec b}\;\,\mathbf{\hat k}} \right]\,\,\mathbf{\hat k} + \left[ {\mathbf{\vec a}\;\;\mathbf{\vec b}\,\;\mathbf{\vec a}\;} \right]

is equal to

View answer and explanation

Correct option: A

2\left( {\mathbf{\vec a}\,\; \times \,\mathbf{\vec b}} \right)\;

Option A (

2\left( \mathbf{\vec a}\,\; \times \\,\mathbf{\vec b}} \right)\,

) is correct because the expression simplifies to twice the cross product of the vectors

\vec{a}

and

\vec{b}