1. Consider two points in space A = (2,1,3) and B = (1,0, – 1), and let a' and b represent the vectors OA and OB, respectively, where O = (0,0,0) is the origin. (a) Find the coordinate of the fourth vertex of the parallelogram whose other three vertices are O, A, and B. (b) Let c = a' + b, find the unit vectors n, î, and î, in the direction of a, %3D b, and C, respectively. (c) Find the projection of 2 a – 3b onto the x, y and z axis, respectively. (d) Find the angle between 2a - 3 b and the x, y and z axis, respectively.
1. Consider two points in space A = (2,1,3) and B = (1,0, – 1), and let a' and b represent the vectors OA and OB, respectively, where O = (0,0,0) is the origin. (a) Find the coordinate of the fourth vertex of the parallelogram whose other three vertices are O, A, and B. (b) Let c = a' + b, find the unit vectors n, î, and î, in the direction of a, %3D b, and C, respectively. (c) Find the projection of 2 a – 3b onto the x, y and z axis, respectively. (d) Find the angle between 2a - 3 b and the x, y and z axis, respectively.
Related questions
Question
Transcribed Image Text:1. Consider two points in space A = (2,1,3) and B = (1,0, – 1), and let a' and b represent the
vectors OA and OB , respectively, where O = (0,0,0) is the origin.
(a) Find the coordinate of the fourth vertex of the parallelogram whose other
three vertices are 0, A, and B.
(b) Let c = a' + b, find the unit vectors î, î, and î, in the direction of a',
b, and c, respectively.
(c) Find the projection of 2 a – 3 b onto the x, y and z axis, respectively.
(d) Find the angle between 2 a' – 3 b and the x, y and z axis, respectively.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps
