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February 5th, 2014, 08:24 AM   #1
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3 algebra problems

Hello everybody, I am Francesco and I would be very grateful if someone could show me the solution for those 3 problems. I have many of them and these are just an example for type, so if I understand I can do the rest of my own. I don't find on google an exact answer to my problems, but all the time something similar but never the same :S. Thank you in advance if you can help the fellow here.
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February 5th, 2014, 07:11 PM   #2
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Re: 3 algebra problems

The first problem asks you to find the intersection of two lines in .
The first line is through and .
The vector from the first point to the second can be written as so that each point on the line can be written as or, equivalently, . Notice that when t= 0, this is the first point, and when t= 1, it is the second point, .

Do the same for the second line, using a different "name" for the variable, s, say, instead of t. Set the corresponding coordinates equal and solve for s and t. You will have 4 equations to solve for two unknowns. That is more equation than unknowns because, in general, two lines in 4 dimensions do NOT intersect. However, here, you have one line through points A and B and the second line between A and C so the point where they intersect should be obvious!
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