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Vector Algebra question

2022 · 26 Jul · Shift 1 · Q36

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JEE Main
Mathematics
Vector Algebra
2022 · 26 Jul · Shift 1 · Q36

Vector Algebra question

2022 · 26 Jul · Shift 1 · Q36

JEE MainMathematicsVector AlgebraMCQ+4 / −1

Let

\overrightarrow{\mathrm{a}}=\alpha \hat{i}+\hat{j}-\hat{k}

and

\overrightarrow{\mathrm{b}}=2 \hat{i}+\hat{j}-\alpha \hat{k}, \alpha\gt 0

. If the projection of

\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}

on the vector

-\hat{i}+2 \hat{j}-2 \hat{k}

is 30, then

\alpha

is equal to :

A
$\frac{15}{2}$
B
8
C
$\frac{13}{2}$
D
7

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