A unit vector coplanar with $\widehat {\bf{i}} + \widehat {\bf{j}} + 2{\bf{\hat k}}$ and $\widehat {\bf{i}} + 2\widehat {\bf{j}} + {\bf{\hat k}}$, and perpendicular to $\widehat {\bf{i}} + \widehat {\bf{j}} + {\bf{\hat k}}$ is

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

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

$\left( {\frac{{\widehat {\bf{i}} + \widehat {\bf{j}} + 2{\bf{\hat k}}}}{{\sqrt 6 }}} \right)$

$\left( {\frac{{\widehat {\bf{i}} + \widehat {\bf{j}} + {\bf{\hat k}}}}{{\sqrt 6 }}} \right)$

JEE MATHEMATICS MCQ: SCALAR TRIPLE PRODUCT

1 Hard

1 of 1

Application +4 | -1

A unit vector coplanar with

\widehat \mathbf{i} + \widehat \mathbf{j} + 2\mathbf{\hat k}

and

\widehat \mathbf{i} + 2\widehat \mathbf{j} + \mathbf{\hat k}

, and perpendicular to

\widehat \mathbf{i} + \widehat \mathbf{j} + \mathbf{\hat k}

View answer and explanation

Correct option: A

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

Option A (

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

) is correct because it is a unit vector that is coplanar with the given vectors and perpendicular to

\widehat \mathbf{i} + \widehat \mathbf{j} + \mathbf{\hat k}