1. If A = {1, 2, 3} determine whether each of the following is true or false and give reasons for your
answer.
a) 3 ∈ A
b) 3 ⊂ A
c) {3} ⊂ A
d) ∅ ∈ A
2. Find A ∪ B and A ∩ B if A and B are as follows:
a) A = {2,5,3}, B = {3, 1, 6}
b) A = {a, b, c, d}, B = {d, e, a}
3. If R = {1, 5, 6}, S = {2, 3, 4}, and T = {6, 2} find:
a) R ∩ (S ∪ T)
b) T ∩ (R ∪ S)
c) (R ∪ S) ∩ (R ∪ T)
4. Use the Venn diagram to represent sets R, S, and T. Shade the region that represents each of the
following:
a) (R ∩ S) ∩ T
b) R ∪ (S ∩ T)
c) (R ∩ S) ∪ (R ∩ T)
5. Given the following vectors, kjiA
r
r
r
r
623 −+= and kjiB
r
r
r
r
+−= 34
Compute
r
r
A
B
⋅
,
r
r
A
B
×
and the angle between A and B
6. Determine the values of “a” so that kjiaA
r
r
r
r
+−= 2 and kjaiaB
r
r
r
r
42 −+= are
perpendicular.
7. Find the direction cosines of the line joining the points (3, 2, -4) and (1, -1, 2).
8. Evaluate the following:
a)
(
)
kij
r
r
r
432 −×
b)
(
)
kji
r
r
r
×+ 2
c)
(
)
(
)
jiki
r
r
r
r
242 +×−
SURVEYING ENGINEERING
FERRIS STATE UNIVERSITY
SURE 372 Adjustment Computations 1 Fall 2005/06
Homework #1
