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Vector Algebra question

2023 · 1 Feb · Shift 2 · Q36

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JEE Main
Mathematics
Vector Algebra
2023 · 1 Feb · Shift 2 · Q36

Vector Algebra question

2023 · 1 Feb · Shift 2 · Q36

JEE MainMathematicsVector AlgebraMCQ+4 / −1

Let

\vec{a}=2 \hat{i}-7 \hat{j}+5 \hat{k}, \vec{b}=\hat{i}+\hat{k}

and

\vec{c}=\hat{i}+2 \hat{j}-3 \hat{k}

be three given vectors. If

\overrightarrow{\mathrm{r}}

is a vector such that

\vec{r} \times \vec{a}=\vec{c} \times \vec{a}

and

\vec{r} \cdot \vec{b}=0

, then

|\vec{r}|

is equal to :

A
$\frac{11}{7}$
B
$\frac{11}{5} \sqrt{2}$
C
$\frac{\sqrt{914}}{7}$
D
$\frac{11}{7} \sqrt{2}$

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