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Vector Algebra question

2022 · 28 Jun · Shift 2 · Q35

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JEE Main
Mathematics
Vector Algebra
2022 · 28 Jun · Shift 2 · Q35

Vector Algebra question

2022 · 28 Jun · Shift 2 · Q35

JEE MainMathematicsVector AlgebraMCQ+4 / −1

Let

\overrightarrow a = \alpha \widehat i + 2\widehat j - \widehat k

and

\overrightarrow b = - 2\widehat i + \alpha \widehat j + \widehat k

, where

\alpha \in R

. If the area of the parallelogram whose adjacent sides are represented by the vectors

\overrightarrow a

and

\overrightarrow b

is

\sqrt {15({\alpha ^2} + 4)}

, then the value of

2{\left| {\overrightarrow a } \right|^2} + \left( {\overrightarrow a \,.\,\overrightarrow b } \right){\left| {\overrightarrow b } \right|^2}

is equal to :

A
10
B
7
C
9
D
14

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