Three vector `vec(A)`,`vec(B)`, `vec(C )` satisfy the relation `vec(A)*vec(B)=0`and `vec(A).vec(C )=0`. The vector `vec(A)` is parallel to

Three vectors satisfy the relation vec(A).vec(B)=0 and vec(A).vec(C )=0 , then vec(A) is parallel to

Vector vec x satisfying the relation vec A*vec x=c and vec B xxvec x=vec B is :

Three vectors vec(a),vec(b) and vec( c ) satisfy the condition vec(a)+vec(b)+vec( c )=vec(0) . Evaluate the quantity mu=vec(a).vec(b)+vec(b).vec( c )+vec( c ).vec(a) , if |vec(a)|=1,|vec(b)|=4 and |vec( c )|=2 .

If the vectors vec(a), vec(b) and vec(c ) satisfy the condition vec(a)+vec(b)+vec(c )=vec(0) and |vec(a)|=3, |vec(b)| =4 and |vec(c )|=5 , then show that vec(a).vec(b)+vec(b).vec(c )+vec(c ). vec(a)=-25 .