1. Determine if the following equations represent the same line
L1=(0,-2,3) + t(-1,1,2)
L2=(-1,1,1)+ v(-2,2,-4)
Supposed to be square bracklets.
The lines aren't even parallel, ....
(-2,2,-4) is not a multiple of (-1,1,2) , so there is no need to go further.
They are not the same line
Hehe Galu
To determine if the two equations represent the same line, we need to compare the direction vectors.
For L1, the direction vector is (-1,1,2).
For L2, the direction vector is (-2,2,-4).
To determine if the direction vectors are the same, we can check if the components of one vector are proportional to the components of the other vector.
To do this, we can set up a proportion using one component from each vector:
(-1) / (-2) = 1 / 2
The proportion is true, which means the direction vectors are proportional. This indicates that the two lines are parallel.
However, we also need to check if they have the same point of intersection. To do this, we can compare two points on the line. Let's take the point (0,-2,3) from L1 and the point (-1,1,1) from L2.
The coordinates of these two points are not the same. Therefore, L1 and L2 do not represent the same line.