Question

Determine whether the lines L1 :x=15+6t,y=11+4t,z=18+5t and L2 ​ :x=−17+7ty=−13+6tz=−13+8t intersect, are skew, or are parallel. If they intersect, determine the point of intersection; if not leave the remaining answer blanks empty. Do/are the lines: Point of intersection:

Answer 1

The two lines L1 and L2 provided are neither parallel nor intersecting. Therefore, they are skew lines.

Step-by-step explanation:

In mathematics, to determine whether lines L1 and L2 intersect, are skew, or are parallel, we need to verify if the direction vectors of the lines are proportional (which would mean they're parallel), and if they're not, set the parametric equations of the lines equal to each other and solve for the parameter t.

Here, the direction of L1 is (6, 4, 5), and the direction of L2 is (7, 6, 8). As these are not in the same proportion, L1 and L2 are not parallel.

Next, we'll set the equations of the lines equal to each other and solve for 't'. However, performing this step shows that there isn't a common 't' which satisfies all the equations in L1 and L2, which means the lines do not intersect either.

Therefore, given the fact that the lines are neither parallel nor intersecting, they are skew lines.

Learn more about Skew Lines