Prove by vector meathod that in any triangle ABC,a/sinA=b/sinB=c/sinC

Consider a triangle ABC all in order i.e., the direction of vector are in a circular direction, for which the sides let BC= vector a,AC=vector b and AB= vector c,Then a+b+c= 0,then a+b= - c then apply vector product = c× a+ c× B=0 since c×- C=0 as angle between the two is 180. Then c× a= - c× b= b× c the ac sin(π- B)= bc sin(π- A) . Then ac sinB= bc sinA.Then c gets cancelled.we get a÷ sinA= b÷ sinB .Then in similar way a÷ sinA= c÷ sinC.overall we get the required relation i.e. sin rule