Relative to an origin O, the position vectors of the points A, B and C are given by
01 =i- j+2k, OB=-i+ j+ k and OC = j+ 2k respectively. Let Il is the plane
containing OA and OB.
(1)
Show that OA and OB are orthogonal.
(In)
Determine if O1 and OB are independent. Justify your answer.
(ili)
Find a non-zero unit vector n which is perpendicular to the plane I.
(IV)
Find the orthogonal projection of OC onto n.
(v)
Find the orthogonal projection of OC on the plane I.