Question

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

Answer 1

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

Answer 2

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

Answer 3

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?

Answer 4

yes, in that case they are parallel but not coincident