The vertices `A , B , C` of triangle `A B C` have respectively position vectors ` vec a , vec b , vec c` with respect to a given origin `O` . Show that the point `D` where the bisector of `/_A` meets `B C` has position vector ` vec d=(beta vec b+gamma vec c)/(beta+gamma),` where `beta=| vec c- vec a|` and, `gamma=| vec a- vec b|dot` Hence, deduce that incentre I has position vector `(alpha vec a+beta vec b+gamma vec c)/(alpha+beta+gamma)` where `alpha=| vec b- vec c|`