00:01
Question, we want to determine whether the lines l1 and l2 are parallel, skew, or intersecting.
00:05
If they intersect, we're going to find the point of intersection.
00:09
So line 1 is given by x equals 5 minus 12t, y equals 3 plus 9t, and z equals 1 minus 3t, while line 2 is given by 3 plus 8s for the x -coordinate, y equals negative 6s, and z equals 7 plus 2s.
00:27
Well, in order for two lines to intersect, it first has to be true that their x and y coordinates are equal to each other.
00:37
So we would need 5 minus 12t to be equal to 3 plus 8s, and we would also need 3 plus 9t to be equal to negative 6s.
00:53
So we're going to start by taking this bottom equation, and we're going to multiply by four -thirds.
01:00
It's a strange number, but you'll see why we did this in a moment.
01:04
When i do, that becomes 4 plus 36 over 3 is 12t equals negative 24 over 3 equals negative 8s.
01:16
And so we have our 5 minus 12t equaling 3 plus 8s.
01:25
Now, i'm going to add these two equations to each other.
01:29
When we add these to each other, we end up getting that 9 on the left is equal to 0 on the right.
01:38
Now, that's not possible, right? 9 cannot be equal to 0.
01:45
What that means is that my x and y coordinates, they are never matching up this time.
01:51
And since they are never matching up, then these guys cannot intersect...