Science:Math Exam Resources/Courses/MATH152/April 2012/Question 01 (b)

MATH152 April 2012

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Question 01 (b)
Let $S_{1}$ be the plane perpendicular to $\mathbf {n} =[2,1,-1]$ and through the point P=[1,-1,0]. Let $S_{2}$ be the plane through the points A=[1,0,0], B=[-1,2,1], C=[0,1,1]. By L, we denote the line of intersection of $S_{1}$ and $S_{2}$. Determine L in equation form.

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?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
The line must satisfy the equations for each plane. How do we indicate that several linear equations must be true at once?

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Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. From 1(a) we saw that the equations for the planes $S_{1}$ and $S_{2}$ are ${\begin{aligned}2x_{1}+x_{2}-x_{3}&=1\\x_{1}+x_{2}&=1.\end{aligned}}$ These two equations taken together are precisely the equation form of the line since any $x_{1},x_{2}$ and $x_{3}$ that satisfy this will be on both planes and therefore be on the line of intersection.