Vector Trigonometry

Trivium

1. Calculate and sketch any linear combination of two vectors.
2. Given two vectors in space, calculate the measure of the angle formed between them.
3. Given two vectors in space, calculate the vector that results from projecting one onto the other.
4. Given two vectors in space, calculate a vector that is normal to both of them.
5. Given the rectangular coordinates of two points in space, calculate the distance between them and their midpoint.
6. Given the rectangular coordinates of two points in space, determine a parameterization of the line that contains those points.
7. Given a line in space and a point not on that line, compute the distance from the point to that line.
8. Given a plane in space and a point not on that plane, compute the distance from the point to that plane.
9. Given two non-intersecting lines in space compute the closest distance between them.
10. Given a plane in space and a line not parallel to that plane, determine the point at which the line intersects that plane.
11. Given three non-colinear points in space determine an equation for the plane that contains those points.
12. Given two non-parallel planes in space, determine a parameterization of the line along which they intersect.

Problems & Challenges

1. TK