If `abs(vec a +vec b) = abs(vec a -vec b)`prove that a and b are perpendicular.

If vec(a) and vec(b) are two vectors such that |vec(a) + vec(b)| = |vec(a)| , then prove tat 2vec(a) + vec(b) is perpendicular to vec(b) .

If vec a xx vec b = vec c and vec b xx vec c = vec a then

[vec a + vec b vec b + vec c vec c + vec a] =

If |vec(a) + vec(b)| = |vec(a) - vec(b)| then

If |vec a + vec b|^(2) = |vec a|^(2) +|vec b|^(2) , then

If 2 vec a . vec b = |vec a|.|vec b| then the between vec a and vec b is

vec a .[(vec b + vec c) xx (vec a + vec b + vec c)] =

Let vec a, vec b and vec c of magnitudes 3,4 and 5 repectively. If vec a is perpendicular to (vec b + vec c), vec b is perpendicular to (vec c + vec a) and vec c is perpendicular to (vec a + vec b) , then the magnitude of vec a + vec b + vec c is