Thursday, October 9, 2008 CODE 111 Mathematics 1229A
Page 1 Test 1
Student’s Name (Print) Student’s Number
1. If u = (1,−1,2,0,3) and v = (2,1,0,4,−1) then u − v =
A: (3,0,2,4,2) B: (2,−1,0,0,−3) C: (−1,−2,2,−4,4)
D: (1,2,−2,4,−4) E: none of A,B,C,D
2. If u = (2,−1,3,4) and v = (1,5,−1,2) then u •v =
A: 15 B: −15 C: 0 D: −2 E: 2
3. If u = (3,1,−2) and v = (4,1,1) then u × v =
A: (3,−5,−1) B: (3,−11,−1) C: (12,1,−2) D: (12,−1,−2) E: (−1,−5,7)
4. If u = (2,k) and v = (12,3) are orthogonal (perpendicular) then k =
1 1
A: 6 B: − C: D: 8 E: −8
2 2
5. If u = (2,k) and v = (12,3) are collinear (parallel) then k =
A: 6 B: − 1 C: 1 D: 8 E: −8
2 2
6. If v and w are vectors in R , which of the following are always true?
(i) ▯v + w▯ = ▯w + v▯
(ii) ▯v − w▯ = ▯v▯ − ▯w▯
(iii) v × w = −(w × v)
(iv) v • w = w •v
A: (i) and (ii) only B: (i) and (iv) only C: (iii) and (iv) only
D: (ii) and (iii) onlyE: (i), (iii) and (iv) only
7. Find cosθ where θ is the angle between u = (2,−1,−2) and v = (0,3,4).
11 11 7 7
A: − B: C: − D: E: 0
15 15 8 8 Mathematics 1229A CODE 111 Thursday, October 9, 2008
Test 1 Page 2
8. Determine which of the following are true, where i = (1,0,0), j = (0,1,0) and k = (0,0,1).
(i) ▯i + j + k▯ = 3
(ii) i × k = j
(iii) i × i •ki
A: (i) only B: (ii) only C: (iii) only D: none of them E: all of them
9. Find the area of the parallelogram determined by the vectors u = (2,−2,1) and
v = (1,0,−1).
√ √ √ √ √
A: 7 B: 17 C: 78 D: 46 E: 53
10. Find the area of the triangle with vertices (2,0,1),(1,0,1) and (3,0,5).
A: 16 B: 8 C: 4 D: 2 E: 1
11. Find the volume of the parallelepiped with edges given by the vectors u = (1,−2,3),
v = (−1,4,0) and w = (1,−1,−2).
A: 13 B: 11 C: 10 D: 8 E: 7
12. Find a unit vector which is orthogonal (perpendicular) to both u = (2,1,−5) and
v = (−1,0,3).
3 1 1
A: (−3,1,−1) B: − , ,− C: (0,1,0)
11 11 11
D: √3 ,−√ 1 ,√ 1 E: √3 ,√1 ,− √1
11 11 11 11 11 11
13. Determine a vector parallel to the line passing through the points (4,2,3) and (1,−1,0).
A: (4,−2,0) B: (1,−2,0) C: (5,1,3) D: (1,0,−1) E: (1,1,1) Thursday, October 9, 2008 CODE 111

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