Let v = (a, b, c) and let , , and be the angles between v

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Let v = (a, b, c) and let α, β, and γ be the angles between v and the positive x-axis, the positive y-axis, and the positive z-axis, respectively (see figure).

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a. Prove that cos2 α + cos2 β + cos2 γ = 1.

b. Find a vector that makes a 45° angle with i and j. What angle does it make with k?

c. Find a vector that makes a 60° angle with i and j. What angle does it make with k?

d. Is there a vector that makes a 30° angle with i and j? Explain.

e. Find a vector v such that α = β = γ. What is the angle?

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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