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in this video were going to talk about how to find the vector equation parametric equations and symmetric equations of a line if were given the point thats on the line and the vector thats parallel to the line and in another problem were going to talk about how to do the same thing if were given two points on the line so lets go over the basics behind this so lets say we have a 3d coordinate system where this is x y and z and were 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 lets 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 lets extend this point by another vector lets 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
