00:01
This question, we're given two lines.
00:03
We want to investigate whether they are parallel or skewer if they have a common point intersection.
00:08
So for the first line, we have this.
00:12
So i can express it as r is equal to 7 -713 plus t to 236.
00:28
T belongs to real number.
00:30
So this is the direction factor for line 1.
00:33
For line 2, r will be minus 5, minus 12, minus 23.
00:39
Plus s 359 as belongs to real number.
00:46
So this is the direction factor for line 2.
00:49
Now since 2 -36 is not equals to 359, they are not parallel then.
00:59
Line 1 is not parallel to line 2.
01:02
So let's try to find whether they have an intersection point.
01:08
So i'm going to set the x for line 1 to the x.
01:13
For line 2, y for line 1 to y for line 2 and same for z for line 1 to z for line 2.
01:27
So this gives me bs minus 2 t equals to 12, that's the first equation.
01:39
Second one is for the y.
01:46
This gives me 5s minus 3 t equals to 19.
01:52
Third one, the z.
02:00
This gives me 9s minus 6t equals to 36.
02:03
The equation.
02:07
We have to solve two equations at one time, one and two and the other one will be, i'll be solving two and three.
02:20
Now if both pairs of simultaneous equation gives me the same unique s and t, then we'll have a point intersection.
02:31
If they give me different answers or there are no solutions, then there is no point intersection.
02:36
So one and two first...