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

Options

A. `P.q`
B. `(P xx Q)/(P)`
C. `(P.Q)/(Q)`
D. `p.q`

Answer

A

Explanation

Let two vectors P and Q are reprsented be graph as below

Here `Q_(p)` is a vector in the direction of P
There form the right angle tringle , we get
`Cos theta = (Q_(p))/(Q)" "....(i)`
`rArr " "Q_(p) = Q cos theta`
Also , `cos theta = (P.Q)/(PQ ) rArr (Q_(P))/(Q) = (P.Q)/(PQ)`
`rArr " "Q_(p) = (P.Q)/(P) " "........(ii)`
As given that , `hatP` is the unit vector along P ,then
`hatP =(P)/(P)" ".........(iii)`
Putting the value of P from Eq.(iii) to Eq. (ii) , we get
`Q_(p) = hatP.Q`