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a) What is a vector in the plane? How do we represent a vector in the coordinate plane?
b) Find the vector with initial point (2,3) and terminal point (4,10).
c) Let v=〈2,1〉. If the initial point v is placed at P(1,1), where is its terminal point? Sketch several representations of v.
d) How is the magnitude of v=〈a1,a2〉 defined? Find the magnitude of w=〈3,4〉.
e) What are the
f) Let v=〈a1,a2〉 be a vector in the coordinate plane. What is meant by the direction θ of v? What are the coordinates of v in terms of its length and direction? Sketch a figure to illustrate your answer.
g) Suppose that v has length |v|=5 and direction θ=π/6. Express v in terms of its coordinates.
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Chapter 9 Solutions
Algebra and Trigonometry (MindTap Course List)
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