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Exam (elaborations)
Student Solutions Manual Chapter 14 Vector Analysis
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---121January 20252024/2025A+
- 14.1 Introduction and Vector Fields 
Thinking Back 
Work as an integral of force and distance 
Since work is the application of force through a distance, the work is (using integration by parts with 
u = x and dv = sin x dx) 
Z π/2 
0 
x sin x dx = [−x cos x] 
π/2 
0 + 
Z π/2 
0 
cos x dx = 0 + [sin x] 
π/2 
0 = 1. 
Vector geometry 
. Since F(x, y, z) = z(x − y) 
2 
i + 
√y j + k, we have 
F(3, 3, √ 
13) = √ 
13(3 − 3) 
2 
i + 
√ 
3j + k = 
D 
0, √ 
3, 1E 
. 
The norm of this...
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