# 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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