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kenewbie
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Homework Statement
This should be simple, but I can't figure out what I did wrong.
A(1,2,1)
B(1,1,3)
C(-1,1,-1)
D(1,-2,1)
a) Give a "parametric representation" of the plane a which goes through the points A, B and C.
b) Give a "parametric representation" of the plane b which goes through the points B, C and D.
c) Give a representation of the line which describe the intersection between the planes a and b.
d) Calculate the angle between planes a and b.
I'm not sure if the term "parametric representation" looses meaning in translation, but the idea is to give a formula using 2 variables so that all values give describe a point on the plane.
The Attempt at a Solution
a)
Vector AB = [ 0, -1, 2 ]
Vector AC = [ -2, -1, -2 ]
Using point A with vectors AB and AC I get the following representation of the plane:
x = 1 - 2t
y = 2 - s - t
z = 1 + 2s - 2t
But my book says the plane is supposed to be
x = 1 + 2t
y = 2 - s + t
z = 1 + 2s + 2t
This seems to be using vectors AB and CA along with the point A. Why would they use CA? Do I describe the same plane as the book?
b)
Using the point B and vectors BC and BD, i get:
x = 1 - 2s
y = 1 - 3t
z = 3 - 4s -2t
which again is different from the answer in my book, which is
x = 1 + s
y = 1 + 3t
z = 3 + 2s + 2t
c)
I would try to set the x-value of plane a equal to the x-value plane b and so forth, and see what values of t and s that solves for, but since my plane-representations are wrong I get bogus values.
d)
using AB x AC as the normal for plane a and BC x BD as the normal for plane b I get an angle of 43.5 between the planes. My book says 58.4
All help appreciated.
k