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

Step-by-step solution

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 = Q p Q ….(i) ⇒ Q p = Q c o s θ Also, c o s θ = P . Q P Q ⇒ Q p Q = P . Q P Q ⇒ Q p = P . Q P ….(ii) As given that, P is the unit vector along P, then P ^ = P P …(iii) Putting the value of P from Eq.(iii) to Eq.(ii), we get Q p = P . Q