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Vector Algebra question

2019 · 9 Apr · Shift 1 · Q28

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PYQ Library
JEE Main
Mathematics
Vector Algebra
2019 · 9 Apr · Shift 1 · Q28

Vector Algebra question

2019 · 9 Apr · Shift 1 · Q28

JEE MainMathematicsVector AlgebraMCQ+4 / −1

Let

\overrightarrow \alpha = 3\widehat i + \widehat j

and

\overrightarrow \beta = 2\widehat i - \widehat j + 3 \widehat k

. If

\overrightarrow \beta = {\overrightarrow \beta _1} - \overrightarrow {{\beta _2}}

, where

{\overrightarrow \beta _1}

is parallel to

\overrightarrow \alpha

and

\overrightarrow {{\beta _2}}

is perpendicular to

\overrightarrow \alpha

, then

{\overrightarrow \beta _1} \times \overrightarrow {{\beta _2}}

is equal to

A
$3\widehat i - 9\widehat j - 5\widehat k$
B
${1 \over 2}$ ( $- 3\widehat i + 9\widehat j + 5\widehat k$ )
C
$- 3\widehat i + 9\widehat j + 5\widehat k$
D
${1 \over 2}$ ( $3\widehat i - 9\widehat j + 5\widehat k$ )

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