Show that `|vec a| vec b + |vec b| vec a`, is perpendicular to `|vec a| vec b - |vec b| vec a`, for any two non-zero vectors `vec a` and `vec b`.

Show that ( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b)dot

For any vectors vec a vec b , show that |vec a + vec b| le |vec a| + |vec b| .

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

Show that the vectors 2 vec a- vec b+3 vec c , vec a+ vec b-2 vec ca n d vec a+ vec b-3 vec c are non-coplanar vectors (where vec a , vec b , vec c are non-coplanar vectors)

For any non-zero vectors vec(a)andvec(b)vec(a)xxvec(b) is

Find |vec a| and |vec b| if (vec a + vec b).(vec a - vec b) = 3 and 2|vec b| = |vec a| .

Prove that [ vec a, vec b, vec c + vec d] = [ vec a, vec b, vec c] + [ vec a, vec b , vec d] .

If vec a and vec b are two vectors such that vec a + vec b is perpendicular to vec a - vec b ,then prove that |vec a| = |vec b| .

Find | vec a|a n d| vec b|,if( vec a+ vec b)dot( vec a- vec b) = 8 , | vec a|=8| vec b|dot

If vec a and vec b are non - zero vectors and |vec a+ vec b| = |vec a - vec b| , then the angle between vec a and vec b is