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Vector Algebra question

2014 · Shift 1 · Q30

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PYQ Library
JEE Advanced
Mathematics
Vector Algebra
2014 · Shift 1 · Q30

Vector Algebra question

2014 · Shift 1 · Q30

JEE AdvancedMathematicsVector AlgebraMultiple correct+3 / −1

Let

\overrightarrow x ,\overrightarrow y

and

\overrightarrow z

be three vectors each of magnitude

\sqrt 2

and the angle between each pair of them is

{\pi \over 3}

. If

\overrightarrow a

is a non-zero vector perpendicular to

\overrightarrow x

and

\overrightarrow y \times \overrightarrow z

and

\overrightarrow b

is a non-zero vector perpendicular to

\overrightarrow y

and

\overrightarrow z \times \overrightarrow x ,

then

A
$\overrightarrow b = \left( {\overrightarrow b \,.\,\overrightarrow z } \right)\left( {\overrightarrow z - \overrightarrow x } \right)$
B
$\overrightarrow a = \left( {\overrightarrow a \,.\,\overrightarrow y } \right)\left( {\overrightarrow y - \overrightarrow z } \right)$
C
$\overrightarrow a \,.\,\overrightarrow b = - \left( {\overrightarrow a \,.\,\overrightarrow y } \right)\left( {\overrightarrow b \,.\,\overrightarrow z } \right)$
D
$\overrightarrow a = \left( {\overrightarrow a \,.\,\overrightarrow y } \right)\left( {\overrightarrow z - \overrightarrow y } \right)$

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