Plane Math Example 2

Solution

1. 1
   Step 1: Find two vectors in the plane: $\vec{AB} = (1,0,0)$ and $\vec{AC} = (0,1,0)$.
2. 2
   Step 2: The normal to the plane is $\vec{n} = \vec{AB} \times \vec{AC} = (0\cdot0-0\cdot1,\ 0\cdot0-1\cdot0,\ 1\cdot1-0\cdot0) = (0,0,1)$.
3. 3
   Step 3: Plane equation using point A$(0,0,0)$: $0(x-0) + 0(y-0) + 1(z-0) = 0$, giving $z = 0$.
4. 4
   Step 4: Verify: all three points satisfy $z=0$.