If ${\bf{\vec u}},\;{\bf{\vec v}}\;{\rm{and}}\;{\bf{\vec w}}\;$ are three non-coplanar vectors, then (${\bf{\vec u}} + {\bf{\vec v}} - {\bf{\vec w}})\cdot\left[ {\left( {{\bf{\vec u}} - {\bf{\vec v}}} \right) \times \left( {{\bf{\vec v}} - {\bf{\vec w}}} \right)} \right]$ equals

${\bf{\vec u}}\cdot{\bf{\vec v}} \times {\bf{\vec w}}$

${\bf{\vec u}}\cdot{\bf{\vec w}} \times {\bf{\vec v}}$

$3{\bf{\vec u}}\cdot{\bf{\vec v}} \times {\bf{\vec w}}$

JEE MATHEMATICS MCQ: SCALAR TRIPLE PRODUCT

1 Easy

1 of 1

Application +4 | -1

\mathbf{\vec u},\;\mathbf{\vec v}\;\mathrm{and}\;\mathbf{\vec w}\;

are three non-coplanar vectors, then (

\mathbf{\vec u} + \mathbf{\vec v} - \mathbf{\vec w})\cdot\left[ {\left( {\mathbf{\vec u} - \mathbf{\vec v}} \right) \times \left( {\mathbf{\vec v} - \mathbf{\vec w}} \right)} \right]

equals

View answer and explanation

Correct option: B

\mathbf{\vec u}\cdot\mathbf{\vec v} \times \mathbf{\vec w}

Option D (

\mathbf{\vec u}\cdot\mathbf{\vec v} \times \mathbf{\vec w}

) is correct because after expanding and simplifying the triple scalar product, the expression reduces to this form.