3D Geometry · Points on a line at distance

Let

L

be the line

\dfrac{x+1}{2} = \dfrac{y+1}{3} = \dfrac{z+3}{6}

and let

S

be the set of all points

(a, b, c)

L

, whose distance from the line

\dfrac{x+1}{2} = \dfrac{y+1}{3} = \dfrac{z-9}{0}

along the line

L

is 7. Then

\displaystyle\sum_{(a,b,c)\in S}(a + b + c)

is equal to:

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