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April 3rd, 2011, 04:16 AM   #1
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perpendicular line given line of intersection and otherplane

The line of intersection of two perpendicular planes is r=(-1+5t)i +(5-t)j +(7-4t)k. One plane is 5x-3y+7z=29. Find the rectangular equation of the other plane.

I think I need to find 3 points in the desired plane, one being (-1,5,7) but I have no idea how. I don't even know what a norm vector is. Help!
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April 3rd, 2011, 09:28 AM   #2
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Re: perpendicular line given line of intersection and otherp

Well, you should start by learning what a norm vector is. What book are you using?

Do you know what a cross product is?
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April 3rd, 2011, 10:01 AM   #3
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Re: perpendicular line given line of intersection and otherp

no, we haven't learned cross products yet. I'm using a textbook from the 1908s...doesn't seem to help much! How would I start this without needing a norm vector/cross product? (Using a very old-fashioned way?)
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April 3rd, 2011, 10:54 AM   #4
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Re: perpendicular line given line of intersection and otherp

I do believe the old fashioned way is with orthogonal vectors (also called norm vectors) and the cross product. Perhaps you know the dot product? (you must, or what would it mean for vectors or planes to be perpendicular - in fact, how do you define two planes to be perpendicular?) As you are limiting yourself to no mathematical tools, more or less, you can guess and check with vectors on the intended plane. You would check that they are on that plane by dotting them with two independent vectors from the original plane (or using whatever other tool you use to define perpendicular planes).

Happy guessing!
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