怎么不相干呢?
设a=(x1,y1,z1)=x1i+y1j+z1k,b=(x2,y2,z2)=x2i+y2j+z2k,则:
a×b=(x1i+y1j+z1k)×(x2i+y2j+z2k)=x1x2(i×i)+x1y2(i×j)+x1z2(i×k)
+y1x2(j×i)+y1y2(j×j)+y1z2(j×k)+z1x2(k×i)+z1y2(k×j)+z1z2(k×k)
=x1y2k-x1z2j-y1x2k+y1z2i+z1x2j-z1y2i=(y1z2-z1y2)i+(z1x2-x1z2)j+(x1y2-y1x2k)k
这刚好是行列式:
|ijk|
|x1y1z1|的值,是不是呢?
|x2y2z2|