If ` veca , vec b , vec c` are three vectors such that ` veca+ vec b+ vec c= vec0` , then prove that ` vec axx vec b= vec bxx vec c= vec cxx vec a`

Explanation

Since` vec a xx vec a = 0 `


`0+ vec a xx vec b + vec a xx vecc = vec0`


`veca xx vecb +veca xx vecc = vec0 `


`veca xx vecb = -veca xx vecc `


Since `-veca xx vecb =vecc xx veca`


`veca xx vecb = vecc xx veca `


Similarly,


`veca + vecb + vecc=vec0`


...