First slide

Vectors

Question

If $\overset{⇀}{A} + \overset{⇀}{B} = \overset{⇀}{R}$ and $2 \overset{⇀}{A} + \overset{⇀}{B}$ is perpendicular to $\overset{⇀}{B}$ then

Moderate

A

A = R
B

B = 2R
C

B = R
D

B = A

Solution

$\large \vec A + \vec B = \vec R$ given $\large 2\vec A + \vec B$ is perpendicular to $\large \vec B$
$(2\vec A + \vec B ).\vec B = 0 \Rightarrow [\vec A + (\vec A + \vec B )].\vec B = 0$
$(\vec A + \vec R ).\vec B = 0 \Rightarrow \vec A = - \vec R\therefore A = R$ $[\because B\ne 0 and \vec R cannot\; be\; perpendicular\;to\;\vec B]$

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