show that ` A =(vec A. vec A)^(1//2)`.

If vec a,vec b and vec c are mutually perpendicular, show that [vec a*(vec b xxvec c)]^(2)=a^(2)b^(2)c^(2)

If vec(alpha) and vec (beta) are perpendicular to each other , show that | vec(alpha) + vec(beta)|^(2) = |vec(alpha)-vec(beta)|^(2)

For any two vectors vec aa n d vec b , show that (1+| vec a|^2)(1+| vec b|^2)={"("1+ vec a.vec b")"^2| vec a+ vec b+( vec axx vec b)|^2

If vec(a) and vec(b) are perpendicular vectors, show that : (vec(a)+vec(b))^(2)=(vec(a)-vec(b))^(2) .

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

Given that vec x+(1)/((vec p)^(2))(vec p*vec x)vec p=vec q show that vec pvec x=(1)/(2)vec p*vec q and find vec x in terms of vec p and vec q

Show that ( vec axx vec b)^2=| vec a|^2| vec b|^2-( vec adot vec b)^2=| [vec a.vec a, vec a.vec b],[ vec a.vec b, vec b.vec b]|

Show that ( vec axx vec b)^2=| vec a|^2| vec b|^2-( vec adot vec b)^2=| [vec a.vec a, vec a.vec b],[ vec a.vec b, vec b.vec b]|

If ABCD is a parallelogram and vec AB = vec a , vec BC= vec b then show that vec AC = vec a+ vec b and vec BD = vec b- vec a .

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