If `veca` is aunit vector and `(vecx-veca).(vecx+veca)=8`, find `absvecx`.

Given two vectors veca and vecb with | veca| and |vecb| =3 and (veca .vecb) =4 find |veca + vecb| and |veca - vecb| .

Find a unit vector perpendicular to each of vectors (veca + vecb) and ( veca - vecb) where veca = hati+ hatj + hatk and vecb = hati + 2hatj + 3hatk .

If veca and vecb are two vectors such that |veca+vecb|=|veca| then prove that vector 2veca + vecb is perpendicular to vector vecb .

Find a unit vector perpendicular to both veca and vecb .

Find the angle between the vectors veca and vecb if |vecaxx vecb| = sqrt(3) |veca| =2 and |vecb|=1