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.

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- Sep 27th 2009, 12:02 PMskeske1234Cartesian Equation for a plane
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. - Sep 27th 2009, 12:19 PMapcalculus

a) z = 3 will do since all points on the plane will have coordinate z=3.

b)

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

For example,

a=1, c=2, d=-1

x + 2z = -1 is an example.

Good luck!!