MATH 241 – Individual Quiz 1

Your Name:

• This quiz must be completed during class time and is closed book, closed notes. You are not allowed to discuss with others. Please turn in solutions to all of these.

• In order to get full credit, please write all your work, not just the final answer.

1. (3 points) Describe in words the following subset of R^{3}:

{(x, y, z) | x − z = 2}.

2. (3 points) Find the vector of length 3 in the direction of v = ⟨4, 3, 1⟩.

3. (4 points) Let v = A⃗B and w = A⃗C, where A, B, C are three distinct points in the

plane. Match (a) - (d) with (i) - (iv). (Hint: Draw a picture.)

(a)w  (b) − v  (c)w − v  (d)v − w
(i)C⃗B  (ii)C⃗A  (iii)B⃗C  (iv)B⃗A

Bonus Problem: (2 points) If A, B and C are the vertices of triangle, what is A⃗B + B⃗C + C⃗A?