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Homework Help: 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


    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:


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

    So now, the equation looks like this:




    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


    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.
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