Prove Vector Perpendicular

Question

The xy-plane is the set of all points whose coordinates are of the form (x,y,0). Suppose that a vector, drawn in standard position, has it's head in the plane. Prove that this vector is perpendicular to the vector $\hat{z} = j$.

I know that two vectors can be proven to be perpendicular if their dot product is equal to zero. So, for a given vector $\overrightarrow{u}$ drawn in the xy-plane, if $y=0$, it will be perpendicular to $\hat{z}$. However, I'm confused whether this actually answered the prompt?

Answer 1

Given that you know:

1. A general vector in the $xy$ plane is $(x,y,0)$.
2. The vector $\hat z$ is the vector $(0,0,1)$.

What is the dot product of a general vector in the $xy$ plane and $\hat z$ equal to?