Let be a parametrized curve and let be a fixed vector. Assume that is orthogonal to

for all and that is also orthogonal to

Prove that is orthogonal to for all

We are given that and is orthogonal to

Let and

So we have:

Now how do I use this info and prove that is orthogonal to for all ?

Is it possible for anyone to kindly give some hints on how to prove this?