第1个回答 2016-02-11
只需要求aXb即可(“X”是向量的外积).
aXb=|i j k|(||表示按照矩阵的行列式来求,i,j,k表示坐标系的三个单位正交基,只需看成未知量)
于是所求单位向量m=aXb/|aXb|,或n=-m(m、n,都是与a,b垂直的单位向量,只不过方向相反)
第4个回答 2016-02-04
let
the unit vector c =(x,y,z ) ⊥a and b
|c|=1
x^2+y^2+z^2 =1 (1)
a.c=0
2x-4y+z=0 (2)
b.c=0
-2y+2z=0
y-z =0
y=z (3)
sub (3) into (2)
2x-4y+z=0
2x-4z+z=0
x=(3/2)z (4)
sub (3) and (4) into (1)
(9/4)z^2 +z^2 +z^2 =1
(17/4)z^2 =1
z = (2/17)√17 or -(2/17)√17
when z =(2/17)√17, x=(3/17)√17 , y=(2/17)√17
when z =-(2/17)√17, x=-(3/17)√17 , y=-(2/17)√17
c=((3/17)√17 ,(2/17)√17, (2/17)√17) or -((3/17)√17 ,(2/17)√17, (2/17)√17)