求垂直于直线a={2,2,1},b={4,5,3}的单位向量c是多少a和b都是向量,

Question

求垂直于直线a={2,2,1},b={4,5,3}的单位向量c是多少
a和b都是向量,

Answer 1

设c=(x,y,z)
a*c=0
b*c=0
单位向量模:x^2+y^2+z^2=1
(2,2,1)*(x,y,z)>>>2x+2y+z=0
(4,5,3)*(x,y,z)>>>4x+5y+3z=0
整理得:
c1=(1/3,-2/3,2/3)
c2=(-1/3,2/3,-2/3)