顯然有
a點乘b = 0
則有向量a和b垂直
已知x=向量a+(t^2-3)b,y=-ka+tb,
則有
x點乘y = (a+(t^2-3)b) 點乘(-ka+tb)
=-ka^2 +tab -k(t^2-3)ab +t(t^2-3)b^2
=-ka^2 + t(t^2-3)b^2 (ab =0)
= -10k + t(t^2-3) (a^2 = |a|^2 = 10,b^2= |b|^2 = 1)
=0
所以有
k = t(t^2-3)/10
把k代入k+t^2/t
得到
(t^3 +t^2 -3t)/t
= t^2 + t -3
=(t+1/2)^2 - 13/4
>= 13/4
所以最小值為13/4