Find A – B for the following cases: (a) A = 6 units, east and B = 4 units, west; and (b) A = 7.0 m, 60° north of east and B = 5.0 m, east. Sample Problem 2.11 Solution: a. b. A = 6 units, east; -B = 4 units, east A-B=A+ (-B) = 6 units, east + 4 units, east = 10 units, east We use the law of cosines to determine A - B. Let D=A-B. Using the lower half of the parallelogram in the figure, D² = (7.0 m)² + (5.0 m)² -2(7.0 m)(5.0 m) cos 60° D = 6.2 m. Using the law of sines, 6.2 m 7.0 m sin 60 sin 0=78°. Therefore, the difference is 6.2 m, 78° north of west. Practice Exercise 2.11 60° D=A-B W -B = 5.0 m 0 O 60° A = 7.0 m ++E B = 5.0 m S Diagram for Sample Problem 2.11b Find B-A for the vectors given in Sample Problem 2.11. Is vector subtraction commutative?
Find A – B for the following cases: (a) A = 6 units, east and B = 4 units, west; and (b) A = 7.0 m, 60° north of east and B = 5.0 m, east. Sample Problem 2.11 Solution: a. b. A = 6 units, east; -B = 4 units, east A-B=A+ (-B) = 6 units, east + 4 units, east = 10 units, east We use the law of cosines to determine A - B. Let D=A-B. Using the lower half of the parallelogram in the figure, D² = (7.0 m)² + (5.0 m)² -2(7.0 m)(5.0 m) cos 60° D = 6.2 m. Using the law of sines, 6.2 m 7.0 m sin 60 sin 0=78°. Therefore, the difference is 6.2 m, 78° north of west. Practice Exercise 2.11 60° D=A-B W -B = 5.0 m 0 O 60° A = 7.0 m ++E B = 5.0 m S Diagram for Sample Problem 2.11b Find B-A for the vectors given in Sample Problem 2.11. Is vector subtraction commutative?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Based it from Sample Problem then proceed to Practice Exercise. show complete solutions and correct answers
Transcribed Image Text:Find A - B for the following cases: (a) A = 6 units, east and B = 4 units, west; and (b) A = 7.0 m,
60° north of east and B = 5.0 m, east.
Sample Problem 2.11
Solution:
a.
b.
A = 6 units, east; -B = 4 units, east
A-B=A+ (-B) = 6 units, east + 4 units, east
= 10 units, east
We use the law of cosines to determine A - B. Let
D=A-B. Using the lower half of the
parallelogram in the figure,
D² = (7.0 m)² + (5.0 m)² -2(7.0 m)(5.0 m) cos 60°
D = 6.2 m.
Using the law of sines,
6.2 m
sin 60°
7.0 m
sin
0=78°.
Therefore, the difference is 6.2 m, 78° north of west.
Practice Exercise 2.11
60°
D=A-B
W
-B = 5.0 m
0
N
lo
60°
A = 7.0 m
++E
B = 5.0 m
S
Diagram for Sample Problem 2.11b
Find B-A for the vectors given in Sample Problem 2.11. Is vector subtraction commutative?
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