Distance of a vector from a subspace made by equations in Linear Algebra

Question

So I have an exercise which gives my me this subspace : $U = {(x,y,z) ∈ R^3: x - y - z = 0 \text{ and } x + y + z = 0}$

and i have to determine the orthogonal projection of $(3,0,-1)$ which i did, which is $(0,1/2,-1/2)$.

the problem is that I also need to determine the distance between $(3,0,-1)$ and $U$.

I think this should be the magnitude of $(3,0,-1) - (0,1/2,-1/2)$ which gives $\sqrt{\frac{19}{2}}$ but the answer given is $\frac{\sqrt{38}}{2}$. Where did I go wrong?

Any help is appreciated.

Answer 1

Nothing. $\sqrt{\frac{19}{2}}=\frac{\sqrt{38}}{2}$