Texts: For the following questions, show all working in detail.
Consider the vector v = i - 2j - k and choose a point A = (a, b, c) where a, b, and c are three different non-zero digits taken from your student ID (21726571).
(a) Write down the position vector OA to the point A.
(b) Find a vector u which is perpendicular to both v and OA.
(c) Find a plane P which passes through A and is perpendicular to u and write it down in:
(i) equational form
(ii) parametric form
(d) Show that P is parallel to OA.
(e) Find a line L which passes through A and is parallel to v and write it in parametric form.
(f) Explain in words why L and P intersect along L.
NOTE: STUDENT ID - 21726571
For the following questions, show all working in detail.
Choose three different non-zero digits taken from your student ID.
(a) Write down the position vector OA to the point A.
(b) Find a vector u which is perpendicular to both v and OA.
(i) Equational form
(ii) Parametric form
(d) Show that P is parallel to OA.
(e) Find a line L which passes through A and is parallel to u and write it in parametric form.
(f) Explain in words why L and P intersect along L.