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Math Help - Vector

  1. #1
    Member Veronica1999's Avatar
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    Vector

    How long is the shadow cast on the ground (represented by the xy-plane) by a pole that is eight meters tall, given that the Sun's rays are parallel to the vector [5,3,-2]?

    This problem confuses me. Doesn't the location of the pole matter?
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  2. #2
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    Quote Originally Posted by Veronica1999 View Post
    How long is the shadow cast on the ground (represented by the xy-plane) by a pole that is eight meters tall, given that the Sun's rays are parallel to the vector [5,3,-2]?

    This problem confuses me. Doesn't the location of the pole matter?
    let the pole be at the origin of the xy plane, represented by the vector <0,0,8>

    let the vector <5d,3d,-2d> represent a sun ray vector from the top of the pole to the ground.

    <0,0,8> + <5d,3d,-2d> = <5d,3d,8-2d> ... the resulting shadow vector lying on the xy plane.

    since the shadow vector lies on the ground, 8-2d = 0 ...

    <0,0,8> + <20,12,-8> = <20,12,0>

    magnitude of the shadow vector ...

    \sqrt{20^2+12^2+0^2} = 4\sqrt{34} \approx 23.3 \, m
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  3. #3
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    Well, there is one piece of information which is not explicitly given in that assignment: the Sun's rays are all parallel with each other (because the Sun is very far away from us). That's why it doesn't matter where on the xy-plane the pole is.
    Last edited by corsica; June 11th 2011 at 11:23 AM. Reason: grammar error
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  4. #4
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    Re: Vector

    Well, if the pole is in Seattle, Wash., there will be no shadow because the sun will covered by clouds!
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