If `vec(a) and vec(b)` are two vector such that `|vec(a) +vec(b)| =|vec(a)|`, then show that vector `|2a +b|` is perpendicular to `vec(b)`.

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 adot

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+2 vec b is perpendicular to vec a .

If vec(a) and vec(b) are two vectors such that |vec(a) xx vec(b)| = vec(a).vec(b) , then what is the angle between vec(a) and vec(b) .

If two vectors vec(a) and vec (b) are such that |vec(a) . vec(b) | = |vec(a) xx vec(b)|, then find the angle the vectors vec(a) and vec (b)

If vec(a) and vec(b) are two vectors such that |vec(a)|= 2, |vec(b)| = 3 and vec(a)*vec(b)=4 then find the value of |vec(a)-vec(b)|

If vec(a) and vec(b) are two vectors such that |vec(a)| = |vec(b)| = sqrt(2) and vec(a).vec(b) = -1 , then find the angle between them.

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 bdot Then find the value of | vec a+ vec b+ vec c| .

If vec(a) , vec( b) and vec( c ) are unit vectors such that vec(a) + vec(b) + vec( c) = 0 , then the values of vec(a). vec(b)+ vec(b) . vec( c )+ vec( c) .vec(a) is

If vec(a), vec(b) and vec(c) are three vectors such that vec(a) times vec(b)=vec(c) and vec(b) times vec(c)=vec(a)," prove that "vec(a), vec(b), vec(c) are mutually perpendicular and abs(vec(b))=1 and abs(vec(c))=abs(vec(a)) .