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March 23rd, 2012, 03:32 PM   #1
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Vector Question

Hi I was wondering how I could go about doing the following question:

Three of the following represent the same line. Which one DOES NOT?

a) x = (0,0,2) + t(2,6,2)
b) x = (1,2,3) + t(2,6,2)
c) x = (1,2,3) + t(1,3,1)
d) x = (2,5,4) + t(1,3,1)

and the reasoning behind it? I have a few questions but I'm not sure I can post more than one at a time. Thank you!
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March 23rd, 2012, 03:43 PM   #2
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Re: Vector Question

All 4 lines are in the same direction, so the question is which 3 have at least one point in common. Start by noticing b) and c) have the same start, so these must be 2 of the vectors. Now take the differences between starts (b vs. a or b vs. d) and see which are in the same direction as the common direction. You can see that the d) - b) start works, while the a) - b) does not.
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