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Vector Algebra question

2020 · 7 Jan · Shift 2 · Q35

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PYQ Library
JEE Main
Mathematics
Vector Algebra
2020 · 7 Jan · Shift 2 · Q35

Vector Algebra question

2020 · 7 Jan · Shift 2 · Q35

JEE MainMathematicsVector AlgebraMCQ+4 / −1

Let

\overrightarrow a

,

\overrightarrow b

and

\overrightarrow c

be three unit vectors such that

\overrightarrow a + \vec b + \overrightarrow c = \overrightarrow 0

. If

\lambda = \overrightarrow a .\vec b + \vec b.\overrightarrow c + \overrightarrow c .\overrightarrow a

and

\overrightarrow d = \overrightarrow a \times \vec b + \vec b \times \overrightarrow c + \overrightarrow c \times \overrightarrow a

, then the ordered pair,

\left( {\lambda ,\overrightarrow d } \right)

is equal to :

A
$\left( {{3 \over 2},3\overrightarrow a \times \overrightarrow c } \right)$
B
$\left( { - {3 \over 2},3\overrightarrow c \times \overrightarrow b } \right)$
C
$\left( { - {3 \over 2},3\overrightarrow a \times \overrightarrow b } \right)$
D
$\left( {{3 \over 2},3\overrightarrow b \times \overrightarrow c } \right)$

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