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

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

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

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

If |vec(a)+vec(b)|=|vec(a)-vec(b)| , prove that vec(a) and vec(b) are perpendicular.

If |vec a+vec b|=|vec a-vec b|, show that the vectors vec a and vec b are perpendicular to each other.

If vec a and vec b are two vectors such that |vec a|=4,|vec b|=3 and vec a*vec b=6. Find the angle between vec a and vec b

If vec a and vec b are two vectors,such that |vec a|=2,|vec b|=1 and vec a*vec b=1, then find (3vec a-5vec b)*(2vec a+7vec b)

Let vec a,vec b, and vec c are vectors such that |vec a|=3,|vec b|=4 and |vec c|=5, and (vec a+vec b) is perpendicular to vec c,(vec b+vec c) is perpendicular to vec a and (vec c+vec a) is perpendicular to vec b. Then find the value of |vec a+vec b+vec c|

If vec a, vec b, vec c are three mutually perpendicular vectors such that | vec a | = | vec b | = | vec c | then (vec a + vec b + vec c) * vec a =

If vec a and vec b are two vectors such that (vec a+vec b)vec a-vec b=0 find the relation between the magnitudes of vec a and vec b