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 plane parallel vectors

  1. Jun 4, 2013 #1
    1. The problem statement, all variables and given/known data
    The vectors a= <-4,3,3> and b = <2,-6,-5> are parallel to a plane PI and R is a point on
    with position vector <104,8,-6> . Find the Cartesian equation of the plane. What is the
    distance of the plane from the origin?

    2. Relevant equations

    3. The attempt at a solution

    This is my thinking.

    Since we are told the vectors a and b are parallel to the plane if we cross them we can get a vector perpendicular to the plane. We can turn that into a unit vector and dot it with the point r.


    a cross b = <3,-14,18> : call this vector v
    v = √(3^2) + (-14^2)+(18)^2 = 23
    So v(hat) = 1/23<3,-14,18>
    Then to get the equation of the plane we can do

    x dot v(hat) = r dot v(hat)

    <x,y,z> dot 1/23<3,-14,18> = <104,8,-6> dot <1/23<3,-14,18>

    So I got
    3/23x - 14/23y + 18/23z = 92/23
    Then just multiply through to clear out the fraction

    3x - 14y +18z = 92

    and the distance from the plane to the origin is 4 units because r dot v hat is 4
    Did I do this correct?
  2. jcsd
  3. Jun 4, 2013 #2
    Looks good to me
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted