Let ${\bf{\vec a}},{\bf{\vec b}}$ and ${{\bf{\vec c}}}$ be non-zero vectors such that $\left( {{\bf{\vec a}} \times {\bf{\vec b}}} \right) \times {\bf{\vec c}} = - \frac{1}{4}\left| {{\bf{\vec b}}} \right|\left| {{\bf{\vec c}}} \right|{\bf{\vec a}}.$ If $\theta $ is the acute angle between vectors ${{\bf{\vec b}}}$ and ${{\bf{\vec c}}}$, then the angle between ${\bf{\vec a}}\;{\rm{and\;}}{\bf{\vec c}}$ is equal to

JEE MATHEMATICS MCQ: VECTOR TRIPLE PRODUCT

1 Easy

1 of 1

Analyzing +4 | -1

Let

\mathbf{\vec a},\mathbf{\vec b}

and

{\mathbf{\vec c}}

be non-zero vectors such that

\left( {\mathbf{\vec a} \times \mathbf{\vec b}} \right) \times \mathbf{\vec c} = - \frac{1}{4}\left| {\mathbf{\vec b}} \right|\left| {\mathbf{\vec c}} \right|\mathbf{\vec a}.

\theta

is the acute angle between vectors

{\mathbf{\vec b}}

and

{\mathbf{\vec c}}

, then the angle between

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

is equal to

View answer and explanation

Correct option: D

\frac{\pi }{2}

Option D (

\frac{\pi}{2}

) is correct because the given condition implies that the dot product of vectors

\vec{a}

and

\vec{c}

is zero, meaning they are orthogonal.

Practice All Chapter MCQs →

{\mathbf{\hat u}}

{\mathbf{\hat v}}

\mathbf{\hat u}\cdot\mathbf{\hat v} = 0

{\mathbf{\hat r}}

{\mathbf{\hat u}}

{\mathbf{\hat v}}

\mathbf{\vec r} \times \left( {\mathbf{\hat u} \times \mathbf{\hat v}} \right)

\lambda \in \mathrm{R}, \vec{a}=\lambda \hat{i}+2 \hat{j}-3 \hat{k}, \vec{b}=\hat{i}-\lambda \hat{j}+2 \hat{k}

((\vec{a}+\vec{b}) \times(\vec{a} \times \vec{b})) \times(\vec{a}-\vec{b})=8 \hat{i}-40 \hat{j}-24 \hat{k}

|\lambda(\vec{a}+\vec{b}) \times(\vec{a}-\vec{b})|^2

\vec{a}=-\hat{i}-\hat{j}+\hat{k}

\vec{a} \cdot \vec{b}=1

\vec{a} \times \vec{b}=\hat{i}-\hat{j}

\vec{a}-6 \vec{b}

\vec{a}, \vec{b}, \vec{c}

\vec u = \vec a \times (\vec b \times \vec c),\vec v = \vec b \times (\vec c \times \vec a)\,\,\,{\text{and}}\,\,\,\vec w = \vec c \times (\vec a \times \vec b)

a

b

a\, \times (a\, \times (a\, \times (a\, \times b)))

\vec{a}

\hat{i} \times(\vec{a} \times \vec{i})+\hat{j} \times(\vec{a} \times \hat{j})+\hat{k} \times(\vec{a} \times \vec{k})