MATH200 December 2012
• Q1 (a) • Q1 (b) • Q2 • Q3 (a) • Q3 (b) • Q3 (c) • Q4 • Q5 • Q6 (a) • Q6 (b) • Q7 (a) • Q7 (b) • Q7 (c) • Q8 (a) • Q8 (b) • Q9 • Q10 •
Question 01 (b)
Let be the line of intersection of the planes and
(b) Find parametric equations for the line through the point that is perpendicular to the line and parallel to the plane
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!
The line in question, lets call it , has a starting point and a direction vector ,
such that .
In the problem formulation, the point is already given.
What does it mean for to be perpendicular to the line ?
What does it mean for to be parallel to a plane ?
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We are searching for a starting point and a direction vector for a line .
Since, the point lies on the line, we choose
The direction vector must be perpendicular to the direction vector of , such that and are perpendicular.
The direction vector must lie in the plane , then the line is parallel to the plane.
Together, we obtain
With , we choose the vector to be
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