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Math Help - Distance from point to plane

  1. #1
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    Distance from point to plane

    Find the distance from the point [11, -10, 17] to the plane
    -4478 - 283 x + 347 y + 416 z = 0

    and assign your exact answer to the name TheDistance.

    what i did was i multipled the variables in the plane by their corresponding variables in the point, and then divided that answer by the distance or magnitude of the plane. I got 611.1906 but the computer keep saying that this is not the correct value. Anyone has an alternative solution? Thanks.
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  2. #2
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    Quote Originally Posted by purplerain View Post
    Find the distance from the point [11, -10, 17] to the plane
    -4478 - 283 x + 347 y + 416 z = 0

    and assign your exact answer to the name TheDistance.

    what i did was i multipled the variables in the plane by their corresponding variables in the point, and then divided that answer by the distance or magnitude of the plane. <<< what exactly is this? I got 611.1906 but the computer keep saying that this is not the correct value. Anyone has an alternative solution? Thanks.
    I assume that you calculated:
    <br />
d = \dfrac{-4478 - 283 \cdot 11 + 347 \cdot (-10) + 416 \cdot 17}{\sqrt{283^2+347^2+416^2}} = \dfrac{-3989 \cdot \sqrt{41506}}{124516} \approx -6.52661

    The negantive sign of d indicates that the given point and the origin are on different sides of the plane.
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  3. #3
    MHF Contributor Calculus26's Avatar
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    If the equation of a plane is ax + by + cz + d = 0

    Then the distance of a point(x0,y0,z0) to the plane is

    D = |ax0 + by0 + cz0 + d|/sqrt(a^2+b^2+c^2)

    I get 6.527
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  4. #4
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    Oops, yall are right, i recalulated it myself and got approximately 6.480549334. I think the sign should be positive.
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