QuestionQ6 (6 points) Find the general equation of the plane containing the origin and points $P(1,2,3)$ and $Q(1,-1,1)$.

Studdy Solution
Use the normal vector and a point on the plane (e.g., the origin) to find the general equation of the plane.
The general equation of a plane is: $$ax + by + cz = d$$
Substitute the normal vector $\langle 5, 2, -3 \rangle$ and the origin $(0,0,0)$: $$5x + 2y - 3z = 0$$
Since the plane passes through the origin, $d = 0$.
The general equation of the plane is: $$\boxed{5x + 2y - 3z = 0}$$