Question

平面内三点A、B、C共线, =(-2,m), =(n,1), =(5,-1),且⊥,求实数m、n的值.

Answer 1

解:因为A、B、C三点共线,所以=λ.

因为==(7,-1-m),

=(n+2,1-m),

所以(7,-1-m)=λ(n+2,1-m),

即7=λ(n+2),1+m=λ(m-1).

所以mn-5m+n+9=0.                                                           ①

由·=0,得m-2n=0.                                              ②

由①②得m=6,n=3或m=3,n=.