Where Line Meets Plane

Geometry Level 4

Consider a plane passing through the point \((1,2,3)\) with normal vector \((4,5,6)\). Suppose we start at the point \((-1,0,5)\) and travel in the direction of the vector \((-1,-1,2)\) until we intersect the plane.

If the intersection point is \((a,b,c)\), what is \(a+b+c\)?

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