Both of your ideas are good, just go ahead: is a vector orthogonal to both and . Since the orthogonal complement of a plane in is a line, is a directing vector for the line you want. So a parametric equation for this line is: , defined for .
Hi, Im trying to find a parametric equation of a line through (2,3,0) and perpendicular to vectors u = i+2j+3k and v = 3i+4j+5k?
To do this I think i need a parallel vector, how do i get this? is it something to do with the cross product?