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michaelwiggin
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Homework Statement
Find a set of parametric equations for the line passing through the point (1, 0, 1) that is parallel to the plane given by x + y + z = 5, and perpendicular to the line
x = −2 + t, y = 1 + t, z = 2 − t.
Homework Equations
The section deals with distances betweens points, lines, and planes in space, so perhaps:
D (distance between a point and a line in space) = ||PQ x u||/||u||, wherein u is the direction vector for the line, and P is a point on the line (so PQ is a vector between P and the Q not on the line).
D (distance between a plane and a point in space) = |PQ dot n|/||n||, wherein n is a vector normal to the plane, and P is a point on the plane, and Q is the point in space.
The Attempt at a Solution
Well, this problem is number 128 in the textbook section... its the last problem, which in Larson's Calculus (this is the first unit in my MV calc class, btw) usually means that it requires a lot more visualization and logic than the prior ones. So I don't want to look like I didn't try, but all I really have to show for myself is some brainstorming.. I haven't been able to put pen to paper meaningfully. I know that I could use a line parallel to the given line, but I can't figure out how to find that given the perpendicular line provided. If the given plane was perpendicular instead of parallel, it would be easy to find a vector normal to it (which would be parallel to the line I'm trying to find) and work from there. I'm just having a big brain fart, and I don't have time today to grapple with this for an hour like I usually do :\ any tips or suggestions would be very very very appreciated! :) thanks!
-MichaelEdit: P.S., in the equations, |...| is absolute value, and ||...|| is magnitude of the vector.
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