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: Equation of a plane?

  1. Aug 26, 2009 #1
    equation of a plane??

    1. The problem statement, all variables and given/known data

    Find an equation of the plane through the point and perpendicular to the given line.
    (-2, 8, 10)
    x = 4 + t, y = 3t, z = 4 - 4t

    3. The attempt at a solution

    i know the point (-2,8,10) is the starting positon (call it R0)
    i know that N (normal) is perpendicular to R - R0 where R is ending position
    R = (x,y,z) so i said
    R= (4+t,3t,4-4t)
    the N (normal) = (a,b,c) and i dont know how to get these numbers. if i can find out these i can plug it into the scalor equation of a plane formula and be set.

    any help would be great!!
  2. jcsd
  3. Aug 26, 2009 #2


    User Avatar
    Homework Helper

    Re: equation of a plane??

    You need to find the direction of x = 4 + t, y = 3t, z = 4 - 4t, this direction is parallel to the normal of your plane

    eg. x=2t,y=3t,z=t

    [x] [0+2t] [0] [2t] [0] [2]
    [y] = [0+3t] = [0] + [3t] = [0] =t[3]
    [z] [0+t] [0] [t] [0] [1]

    so <2,3,1> is the direction of that line

    Do the same for your line.
  4. Aug 26, 2009 #3


    User Avatar
    Science Advisor

    Re: equation of a plane??

    In general, if vector <A, B, C> is perpendicular the plane and (p,q,r) is a point in the plane, then, for a general point (x,y,z) in the plane, <x- p, y- q, z- r> is a vector in the plane and so <A, B, C>.<x- p, y- q, z- r>= A(x- p)+ B(y- q)+ C(z- r)= 0.

    In your case, a vector in the direction of the line x = 4 + t, y = 3t, z = 4 - 4t is <1, 3, -4>, the coefficients of t in each component.
  5. Aug 26, 2009 #4
    Re: equation of a plane??

    thanks alot everyone. i got in a little study group with a few of my friends and we strugled for a while but finally found it out.
    (5 hours for 30 problems... not too bad) haha
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook