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Homework Help: A plane and a point and another point

  1. Apr 14, 2008 #1
    [SOLVED] A plane and a point and another point

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

    According to the Flat Earth CLub, Earth is a plane described by the equation
    x+y+z = 18
    Also according to the Flat Earth Club, Earth will be destroyed on the day this assignment is due by an explosion that will spontaneously occur at the so-called "armageddon point" A = (1,1,1). It so happens that the school (considered as a point) will be the first place on Earth that is destroyed by this explosion (how sad)



    2. Relevant equations

    a) Calculate the coordinates of the school.
    b)What is the distance between A and the school. What is the distance between A and Earth?


    3. The attempt at a solution

    a. Form the line that passes through point A with a direction vector that is parallel to the normal vector of the plane.
    L: (x,y,z) = (i + j + k) + (i + j + k)t
    = (1 + t)i + (1+t)j + (1+t)k
    Now substitute into the equation of the plane to determine the point of intersection P.
    x = t + 1
    y = t +1
    z = t + 1
    (t+1) + (t+1) + (t +1 ) = 18
    3t + 3 = 18
    3t = 15
    t = 5
    The point P is then (6, 6, 6)



    b. The distance (D) between A and the Earth/Monash Universtiy (P) which are 3-D points, is calculated by:

    D = √[(px-ax)2 + (py-ay)2 + (pz-az)2]

    Where P = (px, py, pz) and A = (ax, ay, az)
    Therefore: P = (6,7,8) and A = (1,1,1) and
    D= √[(6-1)2 + (6-1)2 + (6-1)2
    = √75
    = 8.66
     
  2. jcsd
  3. Apr 14, 2008 #2

    dynamicsolo

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    Homework Helper

    Is your question about this whether you solved it correctly? I believe the answer is 'yes'. You are basically being asked to find the perpendicular distance from A to the place and the point on that plane where the normal line from A meets the plane. And that is just what you have done...
     
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