Subspace of $\mathbb{R}^3$ $\{(x,y,z)\mid 2x^2-8y^2-9z^2\le 1\}$


Why is this not a subspace of $\mathbb{R}^3$?

I know the zero vector is in this set because $ 2(0) - 8(0) - 9(0) \le 1$

But I can't seem to verify if the set is closed under linear combination.

Note: This is NOT for a test/marked assignment, simply practice.
Note that $\displaystyle v=\left(\frac{1}{\sqrt{2}},0,0\right)$ is a vector in this collection. Is $2\cdot v$ in this collection?
I think it's because it's not under R^n by scalar multiplication. If u choose

2(1)-8(1)-9(1) = -15

And if u then multiply by a scalar -1, you get 15 which is not defined in the collection.