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#?

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Answer 1 · 2017-11-21T16:50:10

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#