I have an equation (o+t*d)dot(o+t*d)=r^2 where o is a ray's three dimensional origin, t is a scaler variable representing a ray's distance, d is a ray's three dimensional direction, r is a sphere's radius, and dot is the dot product. How can I solve for t? Please list the steps as well as the answer.

 

This sounds like it belongs in Homework Help.

What is the dot product of any vector with itself?

Can you sketch what the system looks like, at least somewhat? That will help you visualize what it going on.