Math: Scalar Equations of a Plane
posted by Anonymous on .
Find the scalar equation of each of the following planes. State which of the planes, if any, are coincident.
a) r = (8,1,8) + s(5,1,4) + t(3,2,4)
Scalar Equation: 12x  8y  13z = 0

b) r = (2,2,5) + s(3,1,1) + t(4,1,4)
Scalar Equation: 3x + 8y  z + 15 = 0
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*****How do you determine if the planes are the same?

(5,1,4) and (3,2,4) are two direction vectors on the first plane.
So we need a normal to these planes, the crossproduct will give us that.
Which will be (12,8,13)
so the scalar equation will be
12x + 8y + 13z = D
(8,1,8) was given as a point on the plane, so
12(8) + 8(1) + 8(13) = D
D = 0
so the scalar equation is
12x + 8y + 13z = 0
Do the second one the same way.