Prove that `(vec(a)*vec(b))^2<=vec(a)^2*vec(b)^2`.

Prove that (vec(a) + vec(b)) xx (vec(a) - vec(b)) = 2 (vec(b) xx vec(a))

Prove that (vec(a)-vec(b)) xx (vec(a) +vec(b))=2(vec(a) xx vec(b))

Prove that (vec(a)+vec(b)).(vec(a)+vec(b)) = |vec(a)|^(2) + |vec(b)|^(2) , if and only if vec(a) , vec(b) are perpendicular , given vec(a) 1= vec (0) , vec (b) != vec (0)

Prove that |vec(a)xx vec(b)|^(2)=|vec(a)|^(2)|vec(b)|^(2)-(vec(a).vec(b))^(2) =|(vec(a).vec(a),vec(a).vec(b)),(vec(a).vec(b),vec(b).vec(b))| .

Prove that , (vec(a) - vec(b)) xx (vec(a) + vec(b)) = 2 ( vec(a) xx vec(b))

prove that (vec(a)+vec(b)).(vec(a)+vec(b))=|vec(a)|^(2)+|vec(b)|^(2) , if and only if vec(a),vec(b) are perpendicular, given vec(a) ne vec(0), vec(b) ne vec(0) .

Prove that : (vec(a) + vec(b)). { (vec(b)+vec(c))xx (vec(c)+vec(a))}= 2 vec(a) . (vec(b)xxvec(c))

Prove that (vec(A) +2vec(B)) .(2vec(A) - 3vec(B)) = 2A^(2) +AB cos theta - 6B^(2) .

Prove that (vec(A)+2vec(B)).(2vec(A)-3vec(B))=2A^(2)+AB cos theta-6B^(2) .