1 Due on Friday, September 12 MATHEMATICS 226, FALL 2014, PROBLEM SET 11
Due on Friday, September 12
Write clearly and legibly, in complete sentences. You must provide complete explanations for all your solutions; answers without justification, even
if correct, will not be marked. You may discuss the homework with other
students, but the final write-up must be your own.
1. (10 marks) Specify the boundary and the interior of the sets S in 3space whose points (x, y, z) satisfy the given conditions. Is S open,
closed, or neither?
(a) x2 + y 2 + z 2 ≥ 16
(b) z ≥ 0, x2 + (y − 2)2 + z 2 &lt; 1
2. (10 marks) Find all values of t for which the vector v = 4ti − tj + 6k
is perpendicular to the vector w = 2i + (4 − 2t)j + (1 − 2t)k.
3. (10 marks) Find vectors a, b, c in R2 such that the set of points whose
position vector r satisfies the inequalities
r &middot; a ≤ 1, r &middot; b ≤ 1, r &middot; c ≤ 1
is the triangle with vertices (1, 2), (2, −2), (−3, 0).
4. (10 marks) Find two unit vectors each of which makes equal angles
with the vectors u = 4i − j − k, v = i + j, and w = 2i + j + k.
1
c Laba. Not to be copied, used, or revised without explicit written permission from
I.