P and Q are two non-zero vectors inclined to each other at an angle ' θ ' . ‘p’ and ‘q’ are unit vectors along P and Q respectively. The component of Q in the direction of Q will be

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Let two vectors P and Q are represented by graph as below

Here, $Q_{p}$ is a vector in the direction of P.
Then, from the right angle triangle, we get
$c o s θ = \frac{Q_{p}}{Q}$ ….(i)
$\Rightarrow Q_{p} = Q c o s θ$
Also, $c o s θ = \frac{P . Q}{P Q} \Rightarrow \frac{Q_{p}}{Q} = \frac{P . Q}{P Q}$
$\Rightarrow Q_{p} = \frac{P . Q}{P}$ ….(ii)
As given that, P is the unit vector along P, then
$\hat{P} = \frac{P}{P}$ …(iii)
Putting the value of P from Eq.(iii) to Eq.(ii), we get
$Q_{p} = P . Q$

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