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Math Help - find eqaution of a plane

  1. #1
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    find eqaution of a plane

    find the equation of the plane that goes through (1,2,-1) and making equal angles with the positive directions of the coordinate axes
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  2. #2
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    Hello, ramzouzy!

    Find the equation of the plane that goes through (1,2,-1) and
    makes equal angles with the positive directions of the coordinate axes

    This plane is tilted so there is an equilateral triangle in the first octant.
    . . It has normal vector: . \vec{n} \:=\:\langle1,1,1\rangle
    Hence, its equation has the form: . (x-x_1) + (y-y_1) + (z-z_1) \:=\:0


    Since (1,2,-1) is on the plane: . (x-1) + (y-2) + (z+1) \:=\:0

    Therefore: . \boxed{x + y + z \:=\:2}

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