Review for Exam I: Intersection of Two Lines (Question 17)

For question 17, it asks to find the intersection between two lines. To approach this, I followed the example that we did in class (I'm pretty sure the second line should have a different variable other than "t" so I picked "s" in my work) where you take each of the parametric equations and solve for each variable (I've attached a photo of my work) so, once I've done that, I'm unsure of what that tells us about the point of intersection. Furthermore, when graphing the two lines, I found that they were parallel to one another, although I think my math says otherwise. Can someone point me in the right direction?



  • You have found $s$ and $t$ correctly - W00t! Your next step should be to plug $t=-1$ into $\vec{p}(t)$ and/or $s=1$ into $\vec{q}(t)$ to find that the lines intersect at the point $(1,2,3)$.

    Your visualization, however, is not correct. The issue is that you're plugging a point and normal vector into Math3D's Line tool - but that's not how that tool works. The Line tool expects a list of points to draw the line through. If you want a plot to verify your computations, you can generate it as on this Math3D page. The result looks like this:

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