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: Distance between the point and the plane

  1. May 29, 2012 #1
    1. The problem statement, all variables and given/known data
    Determine the distance between the point (10,2,3) and the plane determined by the points A(2,3,0), B(3,1,4), and C(5,2,1).

    3. The attempt at a solution
    What I did was I took (B-A) and (C-B) and then I cross product (B-A) and (C-B) and I got -10i + 11j + 5k. After this step, I took point (10,2,3) x -10i + 11j + 5k and then I got -63. Lastly I use l-63l divide with the magnitude of the cross product which is [tex]\sqrt{(-10)^2 + 11^2 + 5^2}[/tex] and I got some really weird answer which is [tex]\sqrt{246}[/tex] also known as 15.68 and it end up with 63/15.68 = 4.018. I am afraid I have gone extremely wrong.
  2. jcsd
  3. May 29, 2012 #2


    User Avatar
    Science Advisor

    This is an error. The B- A= i- 2j+ 4k and C- B= 2i+ j- 3k and the cross product is
    [tex]\left|\begin{array}{ccc}i & j & k \\ 1 & -2 & 4 \\ 2 & 1 & -3\end{array}\right|= (6- 4)i- (-3- 8)j+ (1+ 4)k= 2i+ 11j+ 5k[/tex]
    Looks like you have a sign error.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook