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Vector Algebra question

2022 · 29 Jul · Shift 1 · Q34

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JEE Main
Mathematics
Vector Algebra
2022 · 29 Jul · Shift 1 · Q34

Vector Algebra question

2022 · 29 Jul · Shift 1 · Q34

JEE MainMathematicsVector AlgebraMCQ+4 / −1

Let

\hat{a}

and

\hat{b}

be two unit vectors such that the angle between them is

\frac{\pi}{4}

. If

\theta

is the angle between the vectors

(\hat{a}+\hat{b})

and

(\hat{a}+2 \hat{b}+2(\hat{a} \times \hat{b}))

, then the value of

164 \,\cos ^{2} \theta

is equal to :

A
$90+27 \sqrt{2}$
B
$45+18 \sqrt{2}$
C
$90+3 \sqrt{2}$
D
$54+90 \sqrt{2}$

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