Homework 1 - due wednesday, June 20, in class

Each problem is worth 10 points.

The following problems are from the textbook: Additionally, solve the following problems:
1. Prove that in any parallelogram the sum of squares of its side-lengths equals the sum of squares of its diagonal-lengths.
Hint: Place a vertex of the parallelogram at the origin of the plane. Restate the problem in terms of vector norms, and finally use exercise 20 (p.19) to complete the proof.
2. What can the intersection of 3 planes in R^3 be? Draw a picture for each possible case. Can one have 3 pairwise non-parallel planes in R^3 whose intersection is empty?
3. Let u and v be any vectors. Show that the set of vectors whose endpoints lie on the line segment joining the endpoints of u and v, is exactly the set of vectors of the form tu+(1-t)v, where t is between 0 and 1.
(As t increases from 0 to 1, tu+(1-t)v "slides" from v to u along the line segment joining their endpoints)