Find mean and variance of $Y=\langle X-\xi,n \rangle$

Question

I have the following homework and having difficulties approaching this:

Let X be a regular normal distribution on a vector space V med center $\xi$ and precision $\langle .,. \rangle$ and let $\eta \neq 0$ be a vector in V

Show that the real random variable $Y=\langle X-\xi,\eta \rangle$ has variance $||\eta||^2$

Any hint/help would be appreciated