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Consider the plane x + 2y – z = 5 and the vector = 2i - 5j + 3k. a) Find a normal vector to the plane. b) What is the angle between i and the vector you found in part (a)? c) What is the angle between ī and the plane?

Consider the plane x + 2y – z = 5 and the vector = 2i - 5j + 3k. a) Find a normal vector to the plane. b) What is the angle between i and the vector you found in part (a)? c) What is the angle between ī and the plane?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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40. Consider the plane x + 2y – z = 5 and the vector i = 2i - 55 + 3k. (a) Find a normal vector to the plane. (b) What is the angle between i and the vector you found in part (a)? (c) What is the angle between ī and the plane?
Transcribed Image Text:40. Consider the plane x + 2y – z = 5 and the vector i = 2i - 55 + 3k. (a) Find a normal vector to the plane. (b) What is the angle between i and the vector you found in part (a)? (c) What is the angle between ī and the plane?
44. (a) Give a vector that is parallel to, but not equal to, ū = 4ĩ +35. (b) Give a vector that is perpendicular to i. 45. For what values of t are ü = tỉ -j +k and i ti +tj – 2k perpendicular? Are there values of 1 for which ū and i are parallel?
Transcribed Image Text:44. (a) Give a vector that is parallel to, but not equal to, ū = 4ĩ +35. (b) Give a vector that is perpendicular to i. 45. For what values of t are ü = tỉ -j +k and i ti +tj – 2k perpendicular? Are there values of 1 for which ū and i are parallel?
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