[" 15.Prove that "(vec a+vec b)*(vec a+vec b)=|vec a|^(2)+|vec b|^(2)," if and only if "vec a,vec b" are perpendicular,"],[" given "vec a!=vec 0,vec b!=vec 0" ."]

Prove that (vec a+vec b)*(vec a+vec b)=|vec a|^(2)+|vec b|^(2) and only if vec a,vec b are perpendicular,given vec a!=vec 0,vec b!=vec 0

Prove that ( veca+ vec b).( vec a+ vecb)= | veca|^2+| vec b|^2 , if and only if vec a ,vec b are perpendicular, given vec a!= vec0, vec b!= vec0

Prove that (vec a + vec b).(vec a + vec b) = | vec a|^(2) + |vec b|^(2) , if and only if vec a, vec b are perpendicualr, given a ne vec 0, b ne vec 0 .

prove that (vec(a)+vec(b)).(vec(a)+vec(b))=|vec(a)|^(2)+|vec(b)|^(2) , if and only if vec(a),vec(b) are perpendicular, given vec(a) ne vec(0), vec(b) ne vec(0) .

Prove that (vec(a)+vec(b)).(vec(a)+vec(b)) = |vec(a)|^(2) + |vec(b)|^(2) , if and only if vec(a) , vec(b) are perpendicular , given vec(a) 1= vec (0) , vec (b) != vec (0)

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

(vec a-vec b) * (vec a + vec b) = 27 and | vec a | = 2 | vec b | find | vec a | and | vec b |

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

For the vector vec(a) and vec (b) if |vec(a) + vec(b)| = |vec(a) - vec(b)| , show that vec(a) and vec (b) are perpendicular

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 .