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leehuan's All-Levels-Of-Maths SOS thread (1 Viewer)

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InteGrand

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So assume all vector equations are a plane unless the vectors are scalar multiples of each other.

Well no. For example, if there were three vectors there and they were what is called linearly independent (which is equivalent to (although not defined as) saying that none of them is in the span of the other two ), then they would end up spanning the whole of ℝ3, rather than just a plane.
 
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Drsoccerball

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hmmm :/ If I pick a different starting point for a vector I get a different answer is it wrong?
 

InteGrand

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hmmm :/ If I pick a different starting point for a vector I get a different answer is it wrong?
No, it's not wrong; you can use any point that lies on the plane, so there are (infinitely) many choices for it. The parametric equation is not unique.
 

Drsoccerball

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But when multiplying by x how do we know x is positive?

Or does it like not matter cause we have a three sided inequality
It really doesn't matter if x is positive it doesnt change anything as you said if its negative the inequalities switch and you are still left with :

 

Paradoxica

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But when multiplying by x how do we know x is positive?

Or does it like not matter cause we have a three sided inequality
To brush up on that technical matter, you have to multiply everything by x^2 to prevent change in sign.
 
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