Hi, can someone just check my answer, please?

Question:

Two subspaces S and T of are given by

.

Obtain a non-trivial quadratic such that .

My reponse:

Let ,

Then .

For membership in S: .

For membership in T: .

From (1), .

From (2), .

Let c = 1.

and .

So is one such non-trivial quadratic.