# Journey Through a Sphere

Geometry Level 5

In the $$xyz$$ coordinate system, suppose we begin at $$(x,y,z) = (2,3,4)$$ and head off in a direction described by the vector $$(vx,vy,vz) = (-3,-6,-7)$$.

Along the way, there are two points at which we intersect a unit sphere centered at the origin. What is the distance between the two points of intersection?

Details and Assumptions: