JEE MATHEMATICS MCQ: VECTOR TRIPLE PRODUCT

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Application +4 | -1

Let

\vec{p}, \vec{q}, \vec{r}

be three mutually perpendicular vectors of the same magnitude. If a vector

\vec{x}

satisfies the equation

\vec{p} \times(\vec{x}-\vec{q}) \times \vec{p}\}+\vec{q} \times(\vec{x}-\vec{r}) \times \vec{q}\}+\vec{r} \times\{\vec{x}-\vec{p}) \times \vec{r}\}=\overrightarrow{0},

then

\vec{x}

is given by

View answer and explanation

Correct option: B

\frac{1}{2}(\vec{p}+\vec{q}+\vec{r})

Option B (

\frac{1}{2}(\vec{p}+\vec{q}+\vec{r})

) is correct because substituting this value of

\vec{x}

into the given equation makes it equal to

\overrightarrow{0}

, utilizing the mutually perpendicular nature of

\vec{p}, \vec{q}, \vec{r}

More Questions from VECTOR TRIPLE PRODUCT

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{\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})