How to solve 3 unknowns with 2 equations... Watch

AlexJK
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#1
Report Thread starter 7 years ago
#1
I have:
2x + y - z = 0
and
x + y - 2z = 0

Any help would be appreciated, thanks.
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nuodai
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#2
Report 7 years ago
#2
When you have two equations like this there will either be no solutions or infinitely many, depending on whether the planes described by the equations are parallel or not. [Here they're not parallel so there are infinitely many solutions.]

What you should do is proceed as you would normally. You'll end up with one equation in two variables. Here it's easy to eliminate y, so let's say you're left with an equation in x and z. Then you can set x=t and write z in terms of t, and then substitute back for x and z in terms of t to find y in terms of t.
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AlexJK
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#3
Report Thread starter 7 years ago
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Hmm, the question is:
Find a vector that is perpendicular to both:
2i + j - k
and
i + j - 2k
So I just did
(2i + j - k)* (xi + yj + zk) = 0
etc

When I look at the mark scheme it says:
Let z = 1
Is there any reason for this number to be selected?
I assume as there are an infinite number of solutions any 1 of those infinite will do?
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nuodai
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#4
Report 7 years ago
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(Original post by AlexJK)
When I look at the mark scheme it says:
Let z = 1
Is there any reason for this number to be selected?
I assume as there are an infinite number of solutions any 1 of those infinite will do?
Yes; if you let z=t instead then your solution would define a line, and so setting z=1 just chooses any point on the line (which is fine if you only need to give one solution, as here).
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AlexJK
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#5
Report Thread starter 7 years ago
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Thank you very much.
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