Journey Through a Sphere

Geometry Level 4

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:
Give your answer to two decimal places.


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