Vector help(Planes and normals)

[rock.freak667]

Homework Statement

With O as the origin, the points A,B,C have position vectors
i,i+j,i+j+2k
respectively, Find a vector equation of the common perpendicular of the lines AB and OC.
Show that the shortest distance between the lines AB and OC is \frac{2}{5}\sqrt{5}

Find,in the form ax+by+c=d, an equation for the plane containing AB and the common perpendicular of the lines AB and OC.

Homework Equations

Vector formulae.

The Attempt at a Solution

OA=i
OB=i+j
OC=i+j+2k

AB=AO+OB=j

the direction of the common perpendicular is ABxOC = 2i-k

But to get the vector equation I need a point on the line. How do I find that?

(Also, I was never really taught how to do these sorts of vector problems, only ones at AS math level)