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

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,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

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 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)

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

If vec a a n d vec b are two vectors such that vec adot vec b=6, | vec a|=3 a n d | vec b|=4. Write the projection of vec a on vec bdot

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

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 =