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Vector Algebra question

2008 · Shift 2 · Q28

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PYQ Library
JEE Advanced
Mathematics
Vector Algebra
2008 · Shift 2 · Q28

Vector Algebra question

2008 · Shift 2 · Q28

JEE AdvancedMathematicsVector AlgebraMCQ+3 / −1

Let two non-collinear unit vectors

\widehat a

and

\widehat b

form an acute angle. A point

P

moves so that at any time

t

the position vector

\overrightarrow {OP}

(where

O

is the origin) is given by

\widehat a\cos t + \widehat b\sin t.

When

P

is farthest from origin

O,

let

M

be the length of

\overrightarrow {OP}

and

\widehat u

be the unit vector along

\overrightarrow {OP}

. Then :

A
$\widehat u = {{\widehat a + \widehat b} \over {\left| {\widehat a + \widehat b} \right|}}\,\,and\,\,M = {\left( {1 + \widehat a.\,\widehat b} \right)^{1/2}}$
B
$\widehat u = {{\widehat a - \widehat b} \over {\left| {\widehat a - \widehat b} \right|}}\,\,and\,\,M = {\left( {1 + \widehat a.\,\widehat b} \right)^{1/2}}$
C
$\widehat u = {{\widehat a + \widehat b} \over {\left| {\widehat a + \widehat b} \right|}}\,\,and\,\,M = {\left( {1 + 2\widehat a.\,\widehat b} \right)^{1/2}}$
D
$\widehat u = {{\widehat a - \widehat b} \over {\left| {\widehat a - \widehat b} \right|}}\,\,and\,\,M = {\left( {1 + 2\widehat a.\,\widehat b} \right)^{1/2}}$

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