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  4. If the projection of b on a is twice the projection of a on b , then | b | -| a | is equal to

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Q. If the projection of $b$ on $a $ is twice the projection of $a $ on $b $, then $\left| {b} \right|$ -$\left| a \right|$ is equal to

KEAMKEAM 2012Vector Algebra

Solution:

Given,
projection of $b$ on $a =2$ projection of $a$ on $b$
$\therefore \frac{ b \cdot a }{| a |}=\frac{2 a \cdot b }{| b |}$
$ \Rightarrow | b |=2| a |$
$ \therefore | b |-| a | =2| a |-| a | $
$=| a |$