102. The vector $\vec{r}=x \hat{i}+y \hat{\jmath}+z \hat{k}$, called the position vector points from the origin $(0,0,0)$ to an arbitrary point in space with coordinates $(x, y, z)$. Use what you know about vectors to prove the following: All points $(x, y, z)$ that satisfy the equation $A x+B y+C z=0$, where $A, B$, and $C$ are constants, he in a plane that passes through the origin and that is perpendicular to the vector $A \hat{\imath}+B \hat{\jmath}+C k$. Sketch this vector and the plane.

 102. The vector $\vec{r}=x \hat{i}+y \hat{\jmath}+z \hat{k}$, called the position vector points from the origin $(0,0,0)$ to an arbitrary point in space with coordinates $(x, y, z)$. Use what you know about vectors to prove the following: All points $(x, y, z)$ that satisfy the equation $A x+B y+C z=0$, where $A, B$, and $C$ are constants, he in a plane that passes through the origin and that is perpendicular to the vector $A \hat{\imath}+B \hat{\jmath}+C k$. Sketch this vector and the plane.