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9. Find a unit vector perpendicular to both [1,2,-3] and [2, -1, 4].

9. Find a unit vector perpendicular to both [1,2,-3] and [2, -1, 4].

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.3: Lines And Planes
Problem 32EQ
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Help with question 9 plz
6. Calculate the dot product of each pair of vectors. a) a = [-1, 5] and b = [3, 2] b) = [0, -4] and a = [6, -5] c) e = 5 7. Find two unit vectors parallel to each of the following vectors: a) [-8, 2] b) [9, -3, -5] c) 57-77 + 2k 8. Determine the value of k which satisfies each of the following cond a) [-5, k, 3] and [1, 2, -7] are orthogonal. b) The angle between [6, k, -1] and [3, 4, -2] is 60°. c) The magnitude of [2, k, -7] is 8. 9. Find a unit vector perpendicular to both [1,2,-3] and [2, -1, 4]. 10. a = [-1, 5,2], b = [3, 2,-6], and c = [1, -4,-2]. Calculate the followi a) ảxb b) a. bxc c) |à - b² + 2ả b − |b|² 11. R(1,1,3), S(3,-3,6) and U(-2,4,7) are three vertices of parallelogra a) Find the coordinates of T. b) Find all interior angles of the parallelogram. c) Find the area of the parallelogram.
Transcribed Image Text:6. Calculate the dot product of each pair of vectors. a) a = [-1, 5] and b = [3, 2] b) = [0, -4] and a = [6, -5] c) e = 5 7. Find two unit vectors parallel to each of the following vectors: a) [-8, 2] b) [9, -3, -5] c) 57-77 + 2k 8. Determine the value of k which satisfies each of the following cond a) [-5, k, 3] and [1, 2, -7] are orthogonal. b) The angle between [6, k, -1] and [3, 4, -2] is 60°. c) The magnitude of [2, k, -7] is 8. 9. Find a unit vector perpendicular to both [1,2,-3] and [2, -1, 4]. 10. a = [-1, 5,2], b = [3, 2,-6], and c = [1, -4,-2]. Calculate the followi a) ảxb b) a. bxc c) |à - b² + 2ả b − |b|² 11. R(1,1,3), S(3,-3,6) and U(-2,4,7) are three vertices of parallelogra a) Find the coordinates of T. b) Find all interior angles of the parallelogram. c) Find the area of the parallelogram.
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