00:01
Here we are given a pair of lines l1 and l2, and we are asked to show that they are coincident by writing them in parametric form and comparing components.
00:12
So rewriting these in parametric form as a set of equations.
00:18
For x we have negative 2 plus 7s.
00:22
Y is 3 minus 2s, and z equals 4 plus 2s.
00:35
L2 is x equals negative 30 plus 7t, y equals 11 minus 2t, and z equals negative 4 plus 2t.
00:56
And so looking at these two equations here, you can see that all of the coefficients in l1, the s and in l2 on t are the same.
01:11
And this means that the lines are at the very least parallel.
01:14
That is, they're pointing in the same direction.
01:17
But that alone doesn't tell us that the lines are coincident or that they lie on top of each other.
01:24
For that, we have to look at the other terms in these equations, the constants...