The x-axis and y-axis taken together determine a plane known as
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    Introduction To Three Dimensional Geometry
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    Coordinate planes divide the space into _______ octants.

    eight 
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    The x-axis and y-axis taken together determine a plane known as  ____________.

    XOY or the XY-plane.
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    The coordinates of points in the XY-plane are of the form __________.

    (x, y, 0).
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    Find the distance between the following pairs of points:
    (-1, 3, -4) and (1, -3, 4) 
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    left parenthesis straight x subscript 2 comma space straight y subscript 2 comma space straight z subscript 2 right parenthesis left right arrow left parenthesis 1 comma space minus 3 comma space 4 right parenthesis
    Now,         space space CD equals square root of left parenthesis straight x subscript 1 minus straight x subscript 2 right parenthesis squared plus left parenthesis straight y subscript 1 minus straight y subscript 2 right parenthesis squared plus left parenthesis straight z subscript 1 minus straight z subscript 2 right parenthesis squared end root
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    Answer
    Show that the points (-2, 3, 5), (1, 2, 3) and (7, 0, -1) are collinear. 

    Given points are : A(-2, 3, 5), B(1, 2, 3) and C(7, 0, -1)
    Using distance formula, space space space space space AB equals square root of left parenthesis straight x subscript 1 minus straight x subscript 2 right parenthesis squared plus left parenthesis straight y subscript 1 minus straight y subscript 2 right parenthesis squared plus left parenthesis straight z subscript 1 minus straight z subscript 2 right parenthesis squared end root, we have
                                  AB equals square root of left parenthesis negative 2 minus 1 right parenthesis squared plus left parenthesis 3 minus 2 right parenthesis squared plus left parenthesis 5 minus 3 right parenthesis squared end root equals square root of left parenthesis negative 3 right parenthesis squared plus left parenthesis 1 right parenthesis squared plus left parenthesis 2 right parenthesis squared end root
                                       equals square root of 9 plus 1 plus 4 end root equals square root of 14

                                  BC equals square root of left parenthesis 1 minus 7 right parenthesis squared plus left parenthesis 2 minus 0 right parenthesis squared plus left parenthesis 3 plus 1 right parenthesis squared end root space equals space square root of left parenthesis negative 6 right parenthesis squared plus left parenthesis 2 right parenthesis squared plus left parenthesis 4 right parenthesis squared end root
                                       equals space space square root of 36 plus 4 plus 16 end root space equals space square root of 56 space equals space 2 square root of 14

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                                      equals space square root of 81 plus 9 plus 36 end root space equals space square root of 126 space equals space 3 square root of 14
    Now,       AB + BC = square root of 14 plus 2 square root of 14 equals 3 square root of 14 = CA
    Hence, points A, B, C are collinear.

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