How can you sub in the vector equation in to sphere vector equation in this example? (1 Viewer)

cossine

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How can you says that the vector notation of the sphere uses the same r given for the vector intersecting the sphere?
The sphere is not written in vector notation in fact there is no equation of sphere. "a" is the radius in this context which is some constant like 5.

|r| is the distance from the origin. The definition of |r| is as follows, (r dot_product r)^1/2.
 

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