If ${\rm{\vec \alpha }} = 2\,\widehat {{\bf{\dot i}}} + 3\widehat {\,{\bf{\dot j}}} - {\bf{\hat k}},\;\,\,\;{\rm{\vec \beta }} = - \widehat {{\bf{\dot i}}} + 2\,\widehat {{\bf{\dot j}}} - 4\,{\bf{\hat k}},\;\,\,\;{\rm{\vec \gamma }} = \widehat {{\bf{\dot i}}} + \widehat {{\bf{\dot j}}} + {\bf{\hat k}}$, then what is the value of $\left( {{\bf{\vec a}} \times {\bf{\vec b}}} \right)\,\, \cdot \,\,\left( {{\rm{\vec \alpha }} \times {\rm{\vec \gamma }}} \right)\,\,?$

JEE MATHEMATICS MCQ: DOT PRODUCT OF VECTORS

1 Easy

1 of 1

Application +4 | -1

\mathrm{\vec \alpha } = 2\,\widehat {\mathbf{\dot i}} + 3\widehat {\,\mathbf{\dot j}} - \mathbf{\hat k},\;\,\,\;\mathrm{\vec \beta } = - \widehat {\mathbf{\dot i}} + 2\,\widehat {\mathbf{\dot j}} - 4\,\mathbf{\hat k},\;\,\,\;\mathrm{\vec \gamma } = \widehat {\mathbf{\dot i}} + \widehat {\mathbf{\dot j}} + \mathbf{\hat k}

, then what is the value of

\left( {\mathbf{\vec a} \times \mathbf{\vec b}} \right)\,\, \cdot \,\,\left( {\mathrm{\vec \alpha } \times \mathrm{\vec \gamma }} \right)\,\,?

View answer and explanation

Correct option: C

- 74

Option C (-74) is correct because it is the result of calculating the scalar triple product using the given vectors.