1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Planes and parametric equations

  1. Nov 1, 2014 #1
    • OP warned about not using the homework template
    Hi everyone! I'm having some issues with this problem for linear algebra. I understand parametric equations fairly but I'm confused about the unit vector notation

    1) Consider the plane r(s,t)=2i + (t-s) j + (1+3s-5t) k find the z component of the point (2,-1, z0)

    For what values of s and t is this the case?

    I don't really know how to start the problem because it isn't in vector or parametric form like I'm used to.
  2. jcsd
  3. Nov 1, 2014 #2


    Staff: Mentor

    It's easy enough to get from the vector form to the parametric form of this plane.
    Here x = 2, y = t - s, and z = 1 + 3s - 5t, and you're given a point (2, -1, z0).
  4. Nov 1, 2014 #3


    User Avatar
    Science Advisor

    I don't know what you are "used to" but it certainly is in "vector form" and, as Mark44 says, it is easy to convert to parametric form:
    x= 2, y= t- s, z= 1+ 3s- 5t. In order to have [tex](x, y, z)= (2, -1, z_0)[/tex] you must have 2= 2, t- s= -1, and [tex]1+ 3s- 5t= z_0[/tex].

    Perhaps it is the fact that there is not a single "unique" answer that is bothering you?

    There are an infinite number of points, in fact an entire line, with x= 2, y= -1. From t- s= -1, we can get t= s+ 1 and so write [tex]z_0= 1+ 3s- 5(s+ 1)= 1+ 3s- 5s- 5= -4- 2s[/tex]. The set of such points consists of the line x= 2, y= -1, z= -4- 2s, for any s.
  5. Nov 1, 2014 #4
    Thank you for the replies! I left a little something out of the problem, it said find the z component so that it lies on the plane. Wouldn't that make it just one specific point?
  6. Nov 1, 2014 #5


    Staff: Mentor

    Work the problem through and see.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted