Let ${\bf{\vec a}} = 2\widehat {\bf{i}} + \widehat {\bf{j}} + {\bf{\hat k}},\;{\bf{\vec b}} = \widehat {\bf{i}} + 2\widehat {\bf{j}} - {\bf{\hat k}}$ and a unit vector ${{\bf{\vec c}}}$ be coplanar. If ${{\bf{\vec c}}}$ is perpendicular to ${\bf{\vec a}}\;{\rm{and\;}}{\bf{\vec c}}$ is equal to

$ \pm \frac{1}{{\sqrt 2 }}\left( { - \widehat {\bf{j}} + {\bf{\hat k}}} \right)$

$ \pm \frac{1}{{\sqrt 3 }}\left( { - \widehat {\bf{i}} - \widehat {\bf{j}} - {\bf{\hat k}}} \right)$

$ \pm \frac{1}{{\sqrt 5 }}\left( {\widehat {\bf{i}} - 2\;\widehat {\bf{j}}} \right)$

$ \pm \frac{1}{{\sqrt 3 }}\left( {\widehat {\bf{i}} - \widehat {\bf{j}} - {\bf{\hat k}}} \right)$

JEE MATHEMATICS MCQ: VECTOR TRIPLE PRODUCT

1 Easy

1 of 1

Analyzing +4 | -1

Let

\mathbf{\vec a} = 2\widehat \mathbf{i} + \widehat \mathbf{j} + \mathbf{\hat k},\;\mathbf{\vec b} = \widehat \mathbf{i} + 2\widehat \mathbf{j} - \mathbf{\hat k}

and a unit vector

{\mathbf{\vec c}}

be coplanar. If

{\mathbf{\vec c}}

is perpendicular to

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

is equal to

View answer and explanation

Correct option: A

\pm \frac{1}{{\sqrt 2 }}\left( { - \widehat \mathbf{j} + \mathbf{\hat k}} \right)

The correct answer is A (

\pm \frac{1}{{\sqrt 2 }}\left( { - \widehat \mathbf{j} + \mathbf{\hat k}} \right)

) because it represents a unit vector perpendicular to

\vec a

and coplanar with

\vec a

and

\vec b