Show by a numerical example and geometrically also that ` vec axx vec b= vec axx vec c` does not imply ` vec b= vec c `.

Explanation

`Let veca= 3hati+2hatj+5hatk,hatb=6hati+5hatj+8hatk,vecc=3hati+3hatj+3hatk`
`vecaxxvecb=|{:(hati,hatj,hatk),(3,2,5),(6,5,8):}|`
`= (16-25) hati(24-30)hatj+(15-12)hatk`
`=-9hati+6hatj+3hatk`
`vecaxxvecc=|{:(hati,hatj,hatk),(3,2,5),(3,3,3):}|`
`= ( 6-15) hati-(9-15)hathj+ (9-6)hatk=-9hati+6hatj+3hatk`
`vecaxxvecb=vecaxxvecc ,but vecbnevecc`.