(a) Prove that P = cos 1 ax + sin 1 ay and Q = cos 2...

(a) Prove that P = cos θ1 ax + sin θ1 ay and Q = cos θ2 ax + sin θ2 ay are unit vectors in the
xy-plane respectively making angles θ1 and θ2 with the x-axis.
(b) By means of dot product, obtain the formula for cos(θ2 — θ1)- By similarly formulating P and Q, obtain the formula for cos(θ2 + θ1).
(c) If θ is the angle between P and Q, find ½ |P – Q| in terms of θ.