If `vec(a)` and `vec(b)` are perpendicular vectors such that `|vec(a)+vec(b)|=13 and |vec(a)|=5`, find the value of `|vec(b)|`.

If vec(a) and vec(b) are perpendicular vectors |vec(a) + vec(b)| = 13 and |vec(a)| = 5 , find the value of |vec(b)|

If vec(a) and vec(b) are perpendicular vectors, |vec(a)+vec(b)|=3 and |vec(a)|=5 , find the value of |vec(b)| .

If vec(a) and vec(b) are two vector 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)|= 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 perpendicular vectors, show that : (vec(a)+vec(b))^(2)=(vec(a)-vec(b))^(2) .

If vec(a), vec(b)" and "vec(c) are three unit vectors such that vec(a)+vec(b)+vec(c)=vec(O) , find the value of vec(a).vec(b)+vec(b).vec(c)+vec(c).vec(a) .

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 (3 vec(a) - 5vec(b)).(2vec(a) + 7vec(b)) .

Two vectors vec(a) and vec(b) are such that |vec(a)| = 2 , |vec(b)| = 1 and vec(a) . vec(b) = 1 , then find the value of (3 vec(a) - 5 vec(b)).(2 vec(a) + 7vec(b))