∵向量AB⊥BC,∴AB·BC=0,3*1+5-2z=0,z=4,向量BC=(3,1,4),∵AB∈平面ABC,BC∈平面ABC,BP⊥平面ABC,∴向量BP⊥AB,BP⊥BC,BP·AB=0,BP·BC=0,BP=（x-1,y,-3),BP·AB=x-1+5y+6=0,x+5y=-5,BP·BC=3x-3+y-12=0,3x+y=15,x=40/7,y=-15/7,z=4.
