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: Calculus 3 problem: lines and planes in space

  1. Sep 15, 2014 #1
    Let u=<5,-2,3> and v=<-2,1,4>. Find the value of c which will force the vector w=<2c,3,c-1> to lie in the plane of u and v. I did the cross product of u and v, then i crossed u and w, then I equal the product of u and v with what I got for w. But for some reason when I try doing the triple scalar of u,v, and w; it does not give me zero which would prove that w is in the plane of u and v.
  2. jcsd
  3. Sep 16, 2014 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    It will be much easier for us to help you if you post the calculation that got the wrong result. Here's a dot product symbol and a cross product symbol that you can copy and paste: · ×
  4. Sep 16, 2014 #3
    I think you may be doing the problem incorrectly. The scalar triple product formula is a • (b x c). So I do not believe you need to cross u and v and u and w and equate them. I'm not 100% certain though (I'm currently taking calc 3 myself) so perhaps someone can confirm or deny my suspicion.
  5. Sep 16, 2014 #4


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You could just write the equation$$
    \vec w = a\vec u + b\vec v$$out and set the components equal. 3 equations in 3 unknowns.

    Alternatively, and probably easier, just dot ##\vec w## with ##\vec u \times \vec v##, which is normal to the plane, and and set it equal to zero. Then you can just solve for ##c##.
    Last edited: Sep 16, 2014
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted