Project 3 Due Thursday 30 Jan
This is a group project. Problem 1 is worth 4 points, A-H 2 points each.

Projects be stapled together with no dog-eared corners. 
     Unstapled projects will NOT be accepted. 
     All the names of the particpants must be on the projects. 
     Each member needs to fill out a group evaluation form each week. 
     The form is NOT stapled to the project but handed in separately

1. Find parametric equations of a line L which passes through the origin
O(0, 0, 0) and is perpendicular to the plane Ax+By+Cz+D = 0. Find the point
of intersection Q, and use the distance formula to find the distance |OQ|.
Compare with S11.5 equation 8 page 715 when <x1, y1, z1> = <0, 0, 0>.

The following are from HH13.understanding on page 637. ALL of these
statements below are FALSE. Your job is to produce a counter-example for
each of the wrong statements. For example, #1 says there is exactly
one unit vector parallel to a given vector. A counter-example to this
could be <1, 0, 0> and <-1, 0, 0> are parallel to the vector <1, 0, 0>.
A counter-example is an example that shows the statement is false.

In these u, v and w are vectors, c is a scalar. Sometimes 0 is the scalar
zero and sometimes 0 is the vector <0, 0, 0>.

A. (#4) If v and w are vectors, then ||v + w|| = ||v|| + ||w||.
B. (#7) The vector u + v is always larger in magnitude then both u and v.
C. (#8) For any scalar c and vector v, we have ||cv|| = c||v||.
D. (#16) The dot product u dot v is never negative.
E. (#17) If u dot v = 0 then either u = 0 or v = 0. (u, v vectors.)
F. (#18) If the vectors u, v and w are all nonzero, and u dot v = u dot w,
then v = w.
G. (#25) if v is a nonzero vector and v cross u = v cross w, then u = w.
(u, w are vectors.)
H. (#30) It is never true that v cross w = w cross v. (v, w are vectors.)