Question

prove that the dot product of the position vector to any point in the plane and a normal vector is constant?

Answer 1

Question 17924

Let us have any point $(x, y)$ on the plane $xy$ . The position vector will then have coordinates $\vec{r}(x, y, 0)$ , and normal vector will have coordinates $\vec{n}(0, 0, 1)$ . Hence, $\vec{n} \cdot \vec{r} = 0 \cdot x + 0 \cdot y + 1 \cdot 0 = 0$ .