Problem Set 2—Vectors and their Products

Purpose

This problem set reinforces your understanding of vectors and their two product operations.

Background

This problem set is based on material in sections 12.2 through 12.4 of our textbook. We will discuss this material in class between September 11 and September 16.

Activity

Solve each of the following problems:

Problem 1

Exercise 34 in section 12.2 of our textbook (find a vector of length 3 pointing in the direction opposite to ⟨ 1/2, -1/2, -1/2 ⟩).

Problem 2

Exercise 44 in section 12.2 of our textbook (what heading and speed should an airplane have in the presence of a wind in order to fly in a certain direction at a certain speed).

Problem 3

Exercise 2 in section 12.3 of our textbook (find the dot product, magnitudes, cosine of angle between, projection, and length of projection of vectors ⟨ 3/5, 0, 4/5 ⟩ and ⟨ 5, 12, 0 ⟩).

Problem 4

Exercise 18 in section 12.3 of our textbook (show that certain vectors related to points on the circumference of a circle are perpendicular).

Problem 5

Exercise 10 in section 12.4 of our textbook (calculate ⟨ 1, 0, -1 ⟩ × ⟨ 0, 1, 0 ⟩).

Problem 6

Exercise 28e in section 12.4 of our textbook (is it true that c(u×v) = (cu)×v = u×(cv)).

Follow-Up

I will grade this exercise in a face-to-face meeting with you. During this meeting I will look at your solution, ask you any questions I have about it, answer questions you have, etc. Please bring a written solution to the exercise to your meeting, as that will speed the process along.

Sign up for a meeting via Google calendar. If you worked in a group on this exercise, the whole group should schedule a single meeting with me. Please make the meeting 15 minutes long, and schedule it to finish before the end of the “Grade By” date above.