Mathematics 1229A/B Study Guide - Final Guide: Unit Vector, Scantron Corporation, Parallelogram
29 Dec 2018
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Friday, October 2 0 , 2 0 1 7
Page 1 CODE 111 Mathematics 1229A
Test 1
PART A (18 marks)
NOTE: YOUR ANSWERS TO THE PROBLEMS IN PART A MUST BE
INDICATED ON THE SCANTRON SHEET. YOU SHOULD ALSO CIRCLE
YOUR ANSWERS IN THIS BOOKLET.
1.1
mark Let u=(1,−1,2,3) and v=(0,2,−1,2) be vectors in ℜ4.Findthevector2u−3v.
A:(2,−2,4,6) B:(0,−6,3,−6) C:(1,−3,3,1) D:(2,4,1,12) E:(2,−8,7,0)
2.1
mark If u=(1,2,3) and v=(0,1,1), find d(u,v), the distance between vector uand vector v.
A:√14 B:−√14 C:4 D:√6E:−√6
3.1
mark Which one of the following is a unit vector in the opposite direction to u=(2,−1,2)?
A:!2
3,−1
3,2
3"B:!−2
3,1
3,−2
3"C:!−2
√7,1
√7,−2
√7"
D:!2
√7,−1
√7,2
√7"E:!2
9,−1
9,2
9"
4.1
mark Find the value of kfor which the vectors u=(2,k,−1) and v=(−6,12,3) are collinear.
A:−4B:4 C:−5
4D:5
4E:1
4
5.1
mark Let u=2i+j−2kand v=−2i+3j+6k.Findu•v.
A:−4B:19 C:−6D:−13 E:8
6.1
mark For what value of kare the vectors u=(2,−3,−2,k)andv=(−2,3,2,1) orthogonal?
A:17 B:−17 C:1 D:−1E:0
Mathematics 1229A
Test 1 CODE 111 Friday, October 2 0 , 2017
Page 2
7.1
mark If θis the angle between the vectors u=(0,1,2) and v=(1,1,−1), what is the value of
cos θ?
A:1
15 B:−1
15 C:−1
√15
D:1
√15
E:0
8.1
mark Find the area of the parallelogram determined by vectors u=(0,1,−1) and v=(1,2,3).
A:√28 B:√27 C:√23 D:27 E:1
9.1
mark Which one of the following vectors is orthogonal to both of thevectorsu=(0,1,−1) and
v=(1,2,3) (the vectors from question 8)?
A:(5,−1,1) B:(0,1,1) C:(3,2,−1) D:(0,3,−2) E:(5,−1,−1)
10.1
mark Which of the following is/are true for all vectors uand vin ℜ3?
(i)u•v=v•u
(ii)u×v=v×u
(iii)u×u=(0,0,0)
A:(i)only B:(ii)only C:(i)and(ii)only
D:(i)and(iii)only E:allof(i),(ii)and(iii)
11.1
mark Which of the following is a standard form equation for the plane through point P(3,4,1)
with normal vector n=(−2,3,6)?
A:−2x+3y+6z=12 B:−2x+3y+6z=0 C:3x+4y+z=0
D:3x+4y+z=12 E:3x+4y+z=6
12.1
mark Which one of the following vectors is parallel to the plane 2x−5y−z=3?
A:(2,−5,−1) B:(3,1,1) C:(1,2,5) D:(3,1,−2) E:(5,2,−1)
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MATH 1229A/B Full Course Notes
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Document Summary
Note: your answers to the problems in part a must be. Let u = (1, 1, 2, 3) and v = (0, 2, 1, 2) be vectors in 4. If u = (1, 2, 3) and v = (0, 1, 1), nd d(u, v), the distance between vector u and vector v. Find the value of k for which the vectors u = (2, k, 1) and v = ( 6, 12, 3) are collinear. Let u = 2i + j 2k and v = 2i + 3j + 6k. Find the area of the parallelogram determined by vectors u = (0, 1, 1) and v = (1, 2, 3). Which of the following is/are true for all vectors u and v in 3? (i) u v = v u (ii) u v = v u (iii) u u = (0, 0, 0) D: (i) and (iii) only e: all of (i), (ii) and (iii)
