Let → A = ( ^ i + ^ j )and → B = ( 2 ^ i - ^ j ) . The magnitude of a coplanar vector → C such that → A . → C = → B . → C = → A . → B is given by:

Correct answer: C. (5)/(9) If → C = a ^ i + b ^ j then, → A . → C = → A . → B a + b = 1 . . . . . . . ( i ) → B . → C = → A . → B 2a - b = 1 . . . . . . ( ii ) solving equations ( i ) and ( ii ) we get, a = (1)/(3), b = (2)/(3) | → C | = (1)/(9) + (4)/(9) = (5)/(9)

JEE Main 201816 AprilOnline

Exam: JEE Main
Year: 2018
Date: 16 April
Mode: Online
Subject: Physics
Chapter: Mathematics in Physics

JEE Main 2018 · 16 April · Online · Physics · Mathematics in Physics

Let → A = ( ^ i + ^ j )and → B = ( 2 ^ i - ^ j ) . The magnitude of...

Let

\overset{\to}{A} = \left(\overset{^}{i} + \overset{^}{j}\right)and\overset{\to}{B} = ( 2\overset{^}{i} - \overset{^}{j} )

. The magnitude of a coplanar vector

\overset{\to}{C}

such that

\overset{\to}{A} . \overset{\to}{C} = \overset{\to}{B} . \overset{\to}{C} = \overset{\to}{A} . \overset{\to}{B}

is given by:

Options

A $\sqrt{\dfrac{9}{12}}$
B $\sqrt{\dfrac{20}{9}}$
C $\sqrt{\dfrac{5}{9}}$
D $\sqrt{\dfrac{10}{9}}$

Correct answer

C. $\sqrt{\dfrac{5}{9}}$

Step-by-step solution

\overset{\to}{C} = a\overset{^}{i} + b\overset{^}{j}

then,

\overset{\to}{A} . \overset{\to}{C} = \overset{\to}{A} . \overset{\to}{B}

a + b = 1 . . . . . . . ( i )

\overset{\to}{B} . \overset{\to}{C} = \overset{\to}{A} . \overset{\to}{B}

2a - b = 1 . . . . . . ( ii )

solving equations

( i ) and ( ii )

we get,

a = \dfrac{1}{3}, b = \dfrac{2}{3}

\left|\overset{\to}{C}\right| = \sqrt{\dfrac{1}{9} + \dfrac{4}{9}} = \sqrt{\dfrac{5}{9}}

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