(2) V.r a (x-x)+ 00-y0+8e-) d =3 ex ey V×r= a武 a妙 =0 x-x y-y 2-2 (a-7)r -(a:x ay oy -r or or ay oy a Ox ar a.O =a,ex +ayey+ae: =a (注!这里如果没有引入张量。可以采用分量的方法进行证明,如下) 第一项 =axe(x-0+e,0y-y八+e(e-1=a,g or a 同理,a,y =ayey a. =a.e: (a.V)r=a,e,+a,e,+a.e.=a 7(ar) =a×(V×r)+(a.7)r+r×(V×a)+(r.V)a =a×0+(a.7)r+0+0 =(a.7)r -a⑵ ' ' ' ( ) ( ) ( ) 3 r x x y y z z x y z = − + − + − = ' ' ' 0 x y z e e e r xyz x x y y z z = = − − − ( ) ( ) x y z x y z x x y y z z a r a a a r x y z r r r a a a x y z a e a e a e a = + + = + + = + + = (注!这里如果没有引入张量。可以采用分量的方法进行证明,如下) 第一项 [ ( ) ( ) ( )] , , x x x y z x x y y y z z z x x y y z z r a a e x x e y y e z z a e x x r r a a e a a e y z a r a e a e a e a = − + − + − = = = = + + = 同理, 故( ) ( ) ( ) ( ) ( ) ( ) 0 ( ) +0 0 ( ) a r a r a r r a r a a a r a r a = + + + = + + = =