If `vec A,vec B` & `vec A+vec B` are three non-zero vector. Such that `vec A+vec B` is perpendicular to `vec B` then which of one is correct`:`

Let vec a, vec b, vec c be three non-zero vectors such that [vec with bvec c] = | vec a || vec b || vec c | then

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| .

Let vec a,vec b,vec c be three non-zero vectors such that vec c is a unit vector perpendicular to both vec a and vec b. If the between vec a and vec b is pi/6 prove that [vec avec bvec c]^(2)=(1)/(4)|vec a|^(2)|vec b|^(2)

Let vec a,vec b,vec c are three non-zero vectors and vec b is neither perpendicular to vec a nor to vec c and " (vec a timesvec b)timesvec c=vec a times(vec b timesvec c) .Then the angle between vec a and vec c is:

If vec a and vec b are two non- zero vectors such that | vec a + vec b| = |vec a - vec b| , then show that vec a and vec b are perpendicular.

If vec a and vec b are two non-zero vectors such that |vec a xxvec b|=vec a*vec b, then angle between vec a and vec b

If vec a,vec b, and vec c are non-zero vectors such that vec a.vec b=vec a*vec c, then find the geometrical relation between the vectors.

If vec a,vec b and vec c are three non-zero vectors,prove that [vec a+vec b,vec b+vec c,vec c+vec a]=2[vec a,vec b,vec c]

If vec b is a non-zero vector, then projection of vec a on vec b is