Linear Algebra (Parametric Form)

tweety24
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Homework Statement



L1 : x = (0, 1, 2) + s(1, 0, 2)
L2 : x = (4, 2, c) + t(−2, 0, d)

If c = 5 & d = 0, find the point P on L1 and Q on L2 so that the distance between P & Q is the smallest possible.


Homework Equations



the point of intersection?


The Attempt at a Solution



well the lines aren't parallel or identical in this case so they must intersect at some point.
 
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You are thinking about two dimensions. In three dimensions non parallel lines don't have to intersect.
 
oh okayy...so then to start off would i need to find the determinant?
 
lol yeahh i am
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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