Direction angles and cosines Let v = 8a, b, c9 and let a,
Chapter 11, Problem 83(choose chapter or problem)
Direction angles and cosines Let v = 8a, b, c9 and let a, b, and g be the angles between v and the positive x-axis, the positive y-axis, and the positive z-axis, respectively (see figure). z x v y _ _ _ a. Prove that cos2 a + cos2 b + cos2 g = 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 a = b = g. What is the angle? 8
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