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Vector Algebra question

2023 · 11 Apr · Shift 1 · Q37

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JEE Main
Mathematics
Vector Algebra
2023 · 11 Apr · Shift 1 · Q37

Vector Algebra question

2023 · 11 Apr · Shift 1 · Q37

JEE MainMathematicsVector AlgebraMCQ+4 / −1

Let

\vec{a}

be a non-zero vector parallel to the line of intersection of the two planes described by

\hat{i}+\hat{j}, \hat{i}+\hat{k}

and

\hat{i}-\hat{j}, \hat{j}-\hat{k}

. If

\theta

is the angle between the vector

\vec{a}

and the vector

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

and

\vec{a} \cdot \vec{b}=6

, then the ordered pair

(\theta,|\vec{a} \times \vec{b}|)

is equal to :

A
$\left(\frac{\pi}{3}, 3 \sqrt{6}\right)$
B
$\left(\frac{\pi}{3}, 6\right)$
C
$\left(\frac{\pi}{4}, 3 \sqrt{6}\right)$
D
$\left(\frac{\pi}{4}, 6\right)$

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