1. Not finding help here? Sign up for a free 30min 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!

Find the equation for the plane containing the point

  1. May 29, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the equation for the plane containing the point (3,-8,7) and the line

    l(t)=<1,-8,5>+t<3,-2,5>


    2. Relevant equations

    Cross product

    Equation of a plane: A(x-x0)+B(y-y0)+C(z-z0)+D=0


    3. The attempt at a solution

    First I set t=0 in l(t)=<1,-8,5>+t<3,-2,5> to obtain the point (1,-8,5)

    I then proceed to to subtract the given point (3,-8,7) by (1,-8,5) to get a vector <2,0,2>.

    Since I have two vectors, that is, <3,-2,5> and <2,0,2>, I can use the cross product on

    the two vectors to obtain the vector for the plane. By <3,-2,5> x <2,0,2>, I obtained the

    vector <-4,4,4>. Simplifying it would result in <-1,1,1>.

    Thus, using the equation for the plane:

    A(x-x0)+B(y-y0)+C(z-z0)+D=0

    where <A,B,C> = <-1,1,1> and (x0,y0,z0) = (3,-8,7)

    So now, the equation looks like this:

    -(x-3)+(y+8)+(z-7)=0

    -x+3+y+8+z-7=0

    -x+y+z=-4


    I am not even sure if I did it right. This question was a question on my last exam (and the

    only one that I missed). Sadly, my professor did not even post up the solutions. Can anyone

    please see if my results and methods were correct? Thanks! :)
     
    Last edited: May 29, 2010
  2. jcsd
  3. May 29, 2010 #2

    Mark44

    Staff: Mentor

    You can check your answer yourself.
    Does your plane contain the point (3, -8, 7)?
    Is every point in the given line also on your plane?

    If the answers to both questions are yes, then your work is correct.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook