Let a, b and c be non-zero vectors such that $(a \times b) \times c = \frac{1}{3}|b|\,|c|a.$ If $\theta $ is the acute angle between the vector b and c, then $\sin \theta $ is equal to

JEE MATHEMATICS MCQ: VECTOR TRIPLE PRODUCT

1 Easy

1 of 1

Application +4 | -1

Let a, b and c be non-zero vectors such that

(a \times b) \times c = \frac{1}{3}|b|\,|c|a.

\theta

is the acute angle between the vector b and c, then

\sin \theta

is equal to

View answer and explanation

Correct option: A

\frac{{2\sqrt 2 }}{3}

Option A (

\frac{{2\sqrt 2 }}{3}

) is correct because it is the value of

\sin \theta

derived from the given vector equation and the condition that

\theta

is an acute angle.

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})