r = a + λc is equation of line through a in dir of c. r is vector from origin to a point on line and λ is arbitrary parameter. A simple sketch makes this clear.
Let i, j, k be the usual 3 dimensional basis vectors and assume the given line is in i, j plane. Then kXc is normal to the line and in the plane i, j and the equation of the line through point B (location b) normal to the given line is:
r’ = b + λ’(kXc)
EDIT: whoops. line is in general 3d dir. Take a minute to revise. Sorry
(bXc)Xc is perpendicular to c and in plane of b, c. (difficult to see, actually had to ck with a couple of pencils)
r’ = b + λ’[(bXc)Xc]