00:01
In this question, we are asked to find the point of intersection of the given lines.
00:05
And to do that, we simply need to equate the coordinates of the lines.
00:11
And first let's rewrite each line as a single vector.
00:15
The first line is going to be 2 plus t, 1 plus t, 1 plus t, so these are the coordinates of the first line, and the coordinates of the second line are 2 u, then 1 minus u, and u and to find the point of their intersection we need to equate the coordinates and we will get a system of equations 2 plus t equals to 2 u then 1 plus t equals to 1 minus u and 1 plus t equals to u now we need to solve this system of equations we can cancel 1 in the second equation and we'll get that t must be equal to negative u and we will plug in t equals negative u in the first two equations.
01:17
After doing that, we will get that 2 minus u equals to 2 u.
01:24
Recall that we are replacing t in the first and in the third equations by negative u.
01:31
And in the last one we will get 1 minus u equals to you.
01:38
Then from the first equation 2 equals to 3 u and from this first equation 2 equals to 3 u.
01:48
From the last equation, 1 equals to 2u.
01:53
Then from the first equation, u equals to 2 over 3, from the last equation, u equals to 1 over 2.
02:04
And t equals to negative u...