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Vectors: Vector Plane Equation using the Normal
A plane through the point P( –9, 0, 9)
with normal n =
(
8
–3
0
)
has the cartesian equation:
x + y + z + = 0

tickcross


Worked Solution:

If R(x, y, z) is a point in the plane then the vector
->
PR
 = r – p =
(
x
y
z
)
 –
(
–9
0
9
)
 is perpendicular to n =
(
8
–3
0
)
=>
->
PR
.n = 0
<=>(r – p) . n = 0
<=>r.n – p.n = 0
=>8 x – 3 y – (8×(–9) + (–3)×0 + 0×9 = 0
<=>8 x – 3 y + 72 = 0 and z can take any value
or any positive or negative multiple of this equation.

© MEI Produced by Dr Ron Knott, 20 may 2004
tom . button [AT] mei . org . uk 		Test reference: VectorsPlaneNorm.html?ref=7384