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Math Help - Cartesian Equation for a plane

  1. #1
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    Cartesian Equation for a plane

    Determine a cartesian equation for the plane:
    a) the plane through the point (3,-1,3) and perpendicular to the z-axis.
    b) the plane through the points (3,1,-2) and (1,3,-1) and parallel to the y-axis.
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  2. #2
    Senior Member apcalculus's Avatar
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    Quote Originally Posted by skeske1234 View Post
    Determine a cartesian equation for the plane:
    a) the plane through the point (3,-1,3) and perpendicular to the z-axis.
    b) the plane through the points (3,1,-2) and (1,3,-1) and parallel to the y-axis.

    a) z = 3 will do since all points on the plane will have coordinate z=3.

    b)
    Let the equation be:
    ax+ by + cz = d with b=0.

    Plugging in each point, we get the conditions:

    3a - 2c = d
    a -c = d

    2a - c = 0

    c = 2a

    Generally, all planes ax +2a z = d

    For example,
    a=1, c=2, d=-1
    x + 2z = -1 is an example.

    Good luck!!
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