If O be the origin and if the co-ordinates of any two points P_1 and P_2 be respectively (x_1,y_1) ,(x_2,y_2), prove that OP_1 * OP_2 cosP_1OP_2 = x_1x_2 + y_1y_2?

1 Answer
Nov 21, 2017

Coordinates of points

O->(0,0)
P_1->(x_1,y_1)

P_2->(x_2,y_2)

vec(OP_1)=x_1hati+y_1hatj

vec(OP_2)=x_2hati+y_2hatj

Now

vec(OP_1)*vec(OP_2)=OP_1.OP_2cos/_P_1OP_2

=>(x_1hati+y_1hatj)*(x_2hati+y_2hatj)=OP_1.OP_2cos/_P_1OP_2

=>x_1x_2+y_2y_2=OP_1.OP_2cos/_P_1OP_2