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Vector Algebra question

2024 · 30 Jan · Shift 2 · Q42

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JEE Main
Mathematics
Vector Algebra
2024 · 30 Jan · Shift 2 · Q42

Vector Algebra question

2024 · 30 Jan · Shift 2 · Q42

JEE MainMathematicsVector AlgebraMCQ+4 / −1

Let

\vec{a}=\hat{i}+\alpha \hat{j}+\beta \hat{k}, \alpha, \beta \in \mathbb{R}

. Let a vector

\vec{b}

be such that the angle between

\vec{a}

and

\vec{b}

is

\frac{\pi}{4}

and

|\vec{b}|^2=6

. If

\vec{a} \cdot \vec{b}=3 \sqrt{2}

, then the value of

\left(\alpha^2+\beta^2\right)|\vec{a} \times \vec{b}|^2

is equal to

A
85
B
90
C
75
D
95

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