Question

已知P是△ABC所在平面外一点,M是PC中点,且BM=xAB+yAC+zAP（都是向量）,则x+y-z=?

Answer 1

因为 m为pc中点,所以

BM=1/2(BP+BC)

=1/2(BP+1/2(AB+AC))

=1/2(AP-AB+1/2(AB+AC))

=1/2AP-1/4AB+1/4AC

所以 x+y-z=-1/2