# Math Help - lines in space

1. ## lines in space

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?
thanks.

2. Both of your ideas are good, just go ahead: $\vec{u}\times\vec{v}$ is a vector orthogonal to both $\vec{u}$ and $\vec{v}$. Since the orthogonal complement of a plane in $\mathbb{R}^3$ is a line, $\vec{u}\times\vec{v}$ is a directing vector for the line you want. So a parametric equation for this line is: $\lambda\mapsto (2,3,0)+\lambda \vec{u}\times\vec{v}$, defined for $\lambda\in\mathbb{R}$.