A Calculus of Number Based on Spatial Forms

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in this video we're going to talk about how to find the vector equation parametric equations and symmetric equations of a line if we're given the point that's on the line and the vector that's parallel to the line and in another problem we're going to talk about how to do the same thing if we're given two points on the line so let's go over the basics behind this so let's say we have a 3d coordinate system where this is x y and z and we're going to have a generic line now a line is defined by two things we need a point on a line and the direction of the line if we have those two things we could define any line so let's say that we have this point which is it has the values x zero y zero or z naught this is going to be the position vector r naught and let's extend this point by another vector let's call this vector g if we add those two vectors if we take the vector sum of those two vectors it will give us the position vector r which will define the vector equation of the line so r is t