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am1

I think I missed this when listening to the lecture but how did we get x to become (p + tN)?

RyuK

It's like p is the start point, t a scalar, and N is the unit vector along the Normal direction. This represents a line with a start point of p, along the direction of unit vector N, t governs how much along far along the unit vector so can be between (-inf,inf) unless bounded in case of a line segment.