For any two vectors `vec(a)`, `vec(b)` `|vec(a).vec(b)|<=|vec(a)||vec(b)|`

Prove that for any two vectors vec(a) and vec(b), vec(a).(vec(a)xx vec(b))=0 . Is vec(b).(vec(a)xx vec(b))=0 ?

Prove that for any three vectors vec(a), vec(b) and vec(c), [vec(a) + vec(b) vec(b) + vec(c) vec(c) + vec(a)] = 2 [vec(a)vec(b)vec(c)]

Incase of each of the following statements, state whether it is true or false : For any two vectors vec a, vec b : |vec a*vec b| le |vec a||vec b|

For any two vectors vec(a) and vec(b) , prove that |vec(a)+vec(b)|le|vec(a)|+|vec(b)| .

For any three vectors vec(a),vec(b)andvec(c),(vec(a)+vec(b)).(vec(b)+vec(c))xx(vec(c)+vec(a)) is