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Math Help - vector calculus 3D question

  1. #1
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    vector calculus 3D question

    We just started vector calculus and in trying to get us thinking in 3 dimensions, we are asked to describe the set of points whose distance from the x axis is the same as the distance from the zy plane.

    I am thinking that the points would represent a plane parallel with the zy plane with the same dimensions. Can someone tell me if I am even close to right here? I know it is a simple concept but spacial relationships are not simple to me!!!! Thank you FrostKing
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  2. #2
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    Unfortunately, no, you are not even close to right. A plane parallel to the yz plane would have constant x but the distance of each point on the plane to the x axis would NOT be constant.

    Take the general point (x, y, z). Its distance to the yz-plane (that is, the distance from (x,y,z) to (0,y,z)) is just x. Its distance from the x-axis is the distance from (x,y,z) to (x, 0, 0).
    Find that distance and set it equal to x.
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  3. #3
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    Vector 3d question

    So, I need to use (x,y,z) and (x,0,0) and set value equal to x.

    (x-x)^2 + (y - 0)^2 + (z - 0)^2 = x^2 Therefore, x^2 = y^2 + z^2 and x = y + z?????????
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  4. #4
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    Quote Originally Posted by Frostking View Post
    So, I need to use (x,y,z) and (x,0,0) and set value equal to x.

    (x-x)^2 + (y - 0)^2 + (z - 0)^2 = x^2 Therefore, x^2 = y^2 + z^2 and x = y + z?????????
    The first part of your considerations is OK.

    Take those points which have the same perpendicular distance to the x-axis. All those points are located on a circle-line which lies in a plane parallel to the yz-plane. The radius of this circle must be as long as the distance of the circle from the yz-plane.

    If the distance from the yz-plane increases the radius of the circle increases too.

    I've attached a sketch of the situation and I've drawn 2 examples to demonstrate the relationship between the distance from the x-axis (=the radius) and the distance from the yz-plane.
    Attached Thumbnails Attached Thumbnails vector calculus 3D question-equal_dist.png  
    Last edited by earboth; January 7th 2009 at 11:26 AM. Reason: found a typo
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