已知向量a=(2,-3),向量b=(-1,1).若向量ka+b与向量a+b同向,求k的值；求与a+b平行的单位向量

ka+b
=(2k-1,-3k+1)
a+b
=(1,-2)
(ka+b) // (a+b)
=> (-3k+1)/(2k-1) = -2/1
-3k+1=-4k+2
k=1
a+b = (1,-2)
a+b平行的单位向量
= (a+b)/|a+b|
= (1,-2)/√5