Group 1 Due Thursday 11 Jan

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. A regular tetrahedron with sides of length one, has one vertex at the
origin, a second vertex on the positive x-axis, a third vertex in the
xy-plane with a positive y coordinate and the last vertex has a negative
z coordinate. Find the coordinates of the vertices.

2. Using vector operations, find the angle between one side (the edge
not the face) of a cube and the main diagonal.

3. Use vector operations to write the vector v = <1, 2, 3> as a sum of
two vectors, one parallel to vector w = <1, -1, 0> and the other
perpendicular to w.

4. Let u-hat be the unit vector in the direction of <1, 1, 1>, let v-hat
be the unit vector in the direction of <0, 1, -1> and let w-hat be the unit
vector in the direction of <-2, 1, 1>. Find u-hat, v-hat, w-hat and show
they are mutally perpendicular. Is u-hat, v-hat, w-hat  a right hand system?
Is u-hat, v-hat, - w-hat a right hand system?

5. Write j-hat = <0, 1, 0> as a sum of vectors in the u-hat, v-hat and w-hat
directions you found in #4. (That is find the u-hat, v-hat and w-hat
components of the vector j-hat).