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  4. Two vectors A = 3 and B = 4 are perpendicular. Resultant of both these vectors is R. The projection of the vector B on the vector R is

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Q. Two vectors $A = 3$ and $B = 4$ are perpendicular. Resultant of both these vectors is $R$. The projection of the vector $B$ on the vector $R$ is

UPSEEUPSEE 2016

Solution:

Here, $| A |=3,| B |=4$
image
Let $\angle E O P=\phi$, then
$B =R \cos \phi=4$ and $A =R \sin \phi=3$
$\therefore \tan \phi=\frac{3}{4}$
Now, $\cos \phi=\frac{4}{5}$
Projection of $B$ on $O P$ is $| B | \cos \phi$
i.e. $\quad 4 \cos \phi=4 \times \frac{4}{5}=\frac{16}{5}=3.2$