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Math Help - Few 3d problems

  1. #1
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    Few 3d problems

    1.) I have to determine the geometric shape that is described by:

    (x - 1)^2 + y^2 + (z + 2)^2 = 4

    2.) How do I identify a plane that is parallel to the xy-plane, xz-plane or the yz-plane, given

    y = 4, and then:

    z = -1

    I'm assuming, based on the answers in the back of the book, if you're given a specific coordinate, then that is parallel to the other two planes, that is, if given y = 4 then that's parallel to the xz-plane and when given z = -1 that's parallel to the xy-plane, but why?

    Then, it asks for me to sketch a graph.

    3.) Determine the angle between the two given vectors:

    a = 3i + j - 4k; b = -2i + 2j + k

    I'm assuming you use ||a||*||b||cos(theta) ... so find the norm of each of the vectors and then multiply them and then finally find the arccos of that?

    Thanks.
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  2. #2
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    Quote Originally Posted by Ideasman View Post
    1.) I have to determine the geometric shape that is described by:

    (x - 1)^2 + y^2 + (z + 2)^2 = 4
    Consider,
    x^2+y^2+z^2=2^2=4
    This is a sphere with radius 2 at the origin.
    But instead you have a translation,
    x\to x-1 (moved 1 unit to the x positive direction)
    y\to y (unchanged)
    z\to z+2 (moved 2 units to the z negative direction.

    Thus, it is the same sphere centered at,
    (1,0,-2)
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