Let ${\bf{\vec a}} = \widehat {\bf{j}} - {\bf{\hat k}}$ and ${\bf{\vec c}} = \widehat {\bf{i}} - \widehat {\bf{j}} - {\bf{\hat k}}$. Then the vectors ${{\bf{\vec b}}}$ satisfying ${\bf{\vec a}} \times {\bf{\vec b}} + {\bf{\vec c}} = \vec 0$ and ${\bf{\vec a}} \cdot {\bf{\vec b}} = 3$ is

$ - \widehat {\bf{i}} + \widehat {\bf{j}} - 2{\bf{\hat k}}$

$2\widehat {\bf{i}} - \widehat {\bf{j}} + 2{\bf{\hat k}}$

$\widehat {\bf{i}} - \widehat {\bf{j}} - 2{\bf{\hat k}}$

$\widehat {\bf{i}} + \widehat {\bf{j}} - 2{\bf{\hat k}}$

JEE MATHEMATICS MCQ: VECTOR TRIPLE PRODUCT

1 Easy

1 of 1

Application +4 | -1

Let

\mathbf{\vec a} = \widehat \mathbf{j} - \mathbf{\hat k}

and

\mathbf{\vec c} = \widehat \mathbf{i} - \widehat \mathbf{j} - \mathbf{\hat k}

. Then the vectors

{\mathbf{\vec b}}

satisfying

\mathbf{\vec a} \times \mathbf{\vec b} + \mathbf{\vec c} = \vec 0

and

\mathbf{\vec a} \cdot \mathbf{\vec b} = 3

View answer and explanation

Correct option: A

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

Option A (-i + j - 2k) is correct because it satisfies both the cross product and dot product conditions given in the problem.

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})