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Math Help - Planes

  1. #1
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    Planes

    Quote Originally Posted by Question
    The plane 'H'passes through the points

    A(-1, -1, 1), B(4, 2, 1) and C (2, 1, 0).

    (a) Find a vector equation of the line perpendicular to 'H' which passes through the point D (1, 2, 3).

    (b) The perpendicular from D to the plane 'H' meets 'H' at the point E. Find the coordinates of E.

    I understand part(a) but struggling with part(b). Can I have help? Thanks in advance.
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  2. #2
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    Quote Originally Posted by Air View Post
    I understand part(a) but struggling with part(b). Can I have help? Thanks in advance.
    One approach:

    1. Get the Cartesian equation of the plane H: ax + by +cz = d.

    2. Get a parametric equation of the line found in (a): x = x(t), y = y(t), z = z(t).

    3. Substitute x = x(t), y = y(t), z = z(t) into ax + by +cz = d and solve for t.

    4. Substitute the value of t into x = x(t), y = y(t), z = z(t). These are the required coordinates of E.
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