???

? ??? ??? ?
1) ?? : a*b ¡Ô abcos¦Õ (??? ?)
a , b =?? a, b? ?? ; ¦Õ= a, b ??? ?

2) ???? ??
a*b = (a cos ¦Õ )b = a (b cos ¦Õ )
3) ??? ?? ???? : a.b = b.a
- ????? ???? : i.i = j.j = k.k = 1, i.j = j.k = k.i = 0
4) ??? ?? ??????? ?? ??? ??
a.b = (ax i + ay j + az k).(bx i + by j + bz k)
= (ax bx + ay by + az bz )

? ??? ?? ?
1) ?? : a X b¡Ôc (??)
?? : a b sin ¦Õ
?? : ? ?? a, b? ??? ??? ??


2) ???? ??
¢Ù ?? : ? ??? ??? ?????? ??
¢Ú ?? : ????? ???? ?? ? ??? ?????? ??
¢Û ????? ?? ?
ixi = jxj = kxk = 0
ixj = k = -(j x i), j x k = i = -(k x j), k x i = j = -(i x k)

¢Ü ?? ?? ? ???? : a X b = -(bXa)
¢Ý ?? ?? ??????? ?? ???
a¡Á b = (ax i + ay j + az k)¡Á (bx i + by j + bz k)
= (ay bz -az by ) i + (az bx - ax bz ) j + (ax by -ay bx ) k