Determine a cartesian equation for the plane:
a) the plane through the point (3,-1,3) and perpendicular to the z-axis.
b) the plane through the points (3,1,-2) and (1,3,-1) and parallel to the y-axis.
a) z = 3 will do since all points on the plane will have coordinate z=3.
Let the equation be:
ax+ by + cz = d with b=0.
Plugging in each point, we get the conditions:
3a - 2c = d
a -c = d
2a - c = 0
c = 2a
Generally, all planes ax +2a z = d
a=1, c=2, d=-1
x + 2z = -1 is an example.