Let ${\bf{\vec u}} = \widehat {\bf{i}} + \widehat {\bf{j}},\;{\bf{\vec v}} = \;\widehat {\bf{i}} - \widehat {\bf{j}}$ and ${\bf{\vec w}} = \widehat {\bf{i}} + 2\widehat {\bf{j}} + 3{\bf{\hat k}}$. If ${{\bf{\hat n}}}$ is a unit vector such that ${\bf{\vec u}}.{\bf{\hat n}} = 0$ and ${\bf{\vec v}}.{\bf{\hat n}} = 0$, then $\left| {\vec w.{\bf{\hat n}}} \right|$ is equal to

JEE MATHEMATICS MCQ: SCALAR TRIPLE PRODUCT

1 Easy

1 of 1

Application +4 | -1

Let

\mathbf{\vec u} = \widehat \mathbf{i} + \widehat \mathbf{j},\;\mathbf{\vec v} = \;\widehat \mathbf{i} - \widehat \mathbf{j}

and

\mathbf{\vec w} = \widehat \mathbf{i} + 2\widehat \mathbf{j} + 3\mathbf{\hat k}

. If

{\mathbf{\hat n}}

is a unit vector such that

\mathbf{\vec u}.\mathbf{\hat n} = 0

and

\mathbf{\vec v}.\mathbf{\hat n} = 0

, then

\left| {\vec w.\mathbf{\hat n}} \right|

is equal to

View answer and explanation

Correct option: D

The correct answer is 3 because the unit vector

{\mathbf{\hat n}}

is perpendicular to both

\mathbf{\vec u}

and

\mathbf{\vec v}

, and

\left| {\vec w.{\mathbf{\hat n}}} \right|

is calculated using the cross product.