How can you tell if a plane or a vector passes through the origin?

By simply looking at a vector how can I delineate if it passes through the origin or not?|||For a plane, it's very easy. Just make sure you have a constant of zero. Example: x-5y+2z=0, and this passes the origin as (0)-5(0)+2(0)=0.





For a vector, it's pretty easy too. You should check if your given point and your direction vector are multiples of each other. If your equation reads something like





r = (1,2,3) + s(2,4,6), s is any real number, it passes the origin as (1,2,3) is a scalar multiple of (2,4,6).