MATH152 April 2013
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Question B 02 (c)
Let , and . Let be the triangle whose vertices are A,B, and C.
Find the plane P containing in the equation form i.e. in the form
with a,b,c and d specified.
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?
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If a point lies in the plane , then .
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Since the points A, B, and C all lie in the plane P, we have the following equations are satisfied:
Writing these equations as a linear system gives
Row reducing this system such that we have a pivot in each row we get:
So we can see that we have one free parameter. In other words, any specific values of a,b, and c are determined by our choice of d. If we choose d = 1, then a = -2, b = -1, c = 1. Hence, the plane defined by the points A,B and C is
(Note that any constant multiple the planar equation is also a correct answer: e.g. )
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