(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

This should be simple, but I cant 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.

3. 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

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Basic plane-geometry issue

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