I am having trouble understanding how the vector equation of a line : (x,y,z) + t(x1,y1,z1) can be used in conjuction with another vector in the form (x,y,z). I visualise it like this. Points are : O to P and O to Q. So there are two vectors. The vector P to Q is given by Q - P which is the same as (x1,y1,z1). So that means if someone gives me a vector (x2,y2,z2) to determine if it is perpendicular or parallel I can just use (x1,y1,z1) and do the necessary tests dot product = 0 for perp. and cross product = 0 for parallel ? Is my understanding correct ?