Journey Through a Sphere
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.