chrisplusian
  • chrisplusian
Linear algebra..... When you have the equation of two lines how do you show that they are coincident? I realize that you must show that their directional vectors are either the same or scalar multiples, and then you must show a point is the same on one line. The part I don't understand is how you show the point is the same... See attachment
Mathematics
schrodinger
  • schrodinger
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chrisplusian
  • chrisplusian
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IrishBoy123
  • IrishBoy123
pick a point that definitely one 1 line, you do this by setting s or t to zero here they chose s = 0 and found t = 2 gives you the same point they couldhave set t = 0 and solved for s
IrishBoy123
  • IrishBoy123
so if we do set t to zero, we know that (1,3,4) is on line 1 is it on line 2 well solve (1,3,4) = (3,7,2) + s(-3,-6,3) => s = 2/3

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chrisplusian
  • chrisplusian
So this process always works in this type of problem? You just set either the t or s variable equal to zero and solve for the other variable? Does that imply that if you get value for s or t and plug it back in and it does not work out that they are not coincidental?
IrishBoy123
  • IrishBoy123
yes, in that case they are parallel but not coincident

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