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Vector Algebra question

2012 · Shift 0 · Q44

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PYQ Library
JEE Main
Mathematics
Vector Algebra
2012 · Shift 0 · Q44

Vector Algebra question

2012 · Shift 0 · Q44

JEE MainMathematicsVector AlgebraMCQ+4 / −1

Let

ABCD

be a parallelogram such that

\overrightarrow {AB} = \overrightarrow q ,\overrightarrow {AD} = \overrightarrow p

and

\angle BAD

be an acute angle. If

\overrightarrow r

is the vector that coincide with the altitude directed from the vertex

B

to the side

AD,

then

\overrightarrow r

is given by :

A
$\overrightarrow r = 3\overrightarrow q - {{3\left( {\overrightarrow p .\overrightarrow q } \right)} \over {\left( {\overrightarrow p .\overrightarrow p } \right)}}\overrightarrow p$
B
$\overrightarrow r = - \overrightarrow q + {{\left( {\overrightarrow p .\overrightarrow q } \right)} \over {\left( {\overrightarrow p .\overrightarrow p } \right)}}\overrightarrow p$
C
$\vec r = \vec q - {{\left( {\vec p.\vec q} \right)} \over {\left( {\vec p.\vec p} \right)}}\vec p$
D
$\overrightarrow r = - 3\overrightarrow q - {{3\left( {\overrightarrow p .\overrightarrow q } \right)} \over {\left( {\overrightarrow p .\overrightarrow p } \right)}}$

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