A,B,C and D are points of the plane
1)show that :vector 2DA+vector 3DB = zero vector
then AD vector = 3/5 AB vector
Why even mention "C"? We can always set up a coordinate system so that one point, say D, is the origin. Write , in such a coordinate system. The we can represent vector DA as and vector DB as . Then , and 2DA+ 3DB= 0 becomes or and .
In that same system, while .
The result you are asking for, that is the same as and . That is, and .