r=a+ λcis equation of line throughain dir ofc.ris vector from origin to a point on line and λ is arbitrary parameter. A simple sketch makes this clear.

Leti,j,kbe the usual 3 dimensional basis vectors and assume the given line is ini,jplane. ThenkXcis normal to the line and in the planei,jand the equation of the line through point B (locationb) 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)Xcis perpendicular tocand in plane ofb,c. (difficult to see, actually had to ck with a couple of pencils)

r’ =b+ λ’[(bXc)Xc]