The rotation matrix R=rotate the vector v =O [1 2]OO22° [2²]O[2]cos (0)sin (0)Meblesin (0)Cos (0)by an angle of1when multiplied to a vector v, rotates v counter-clockwise by an angle. With this information, we want toin the CLOCKWISE direction. The rotated vector is

The rotation matrix when multiplied to a vector counter clockwise by an angle .Given . The…

Answered: The rotation matrix R= rotate the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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(Question 1] Let A= p' cos(p)a, + sin(ø)a, +z'a, and B=xya, + y'a, + za, find 1. A• Bat (2 2. The angle between the two vectors III
Let u = (-1,2, 3) and v = (-1, 1, –11) be two vectors in R. (a) Calculate the dot product u · v. What does it say about the angle between u and v? (b) Compute the lengths ||u|| and ||v|| of the vectors. (c) Let 6 be the angle between u and v. Find cos 6, where 0< 0
7:EA [Question 1] Let A = p° cos($)a, +sin(ø)a, + z°a¸ and B= xya, + y’a, + za, find 1. A• Bat (2,- 3 6 2. The angle between the two vectors II
3. The geometrical representation of a vector v = is an arrow starting at the origin and ending at the point (a, b). cos 0 - sin e Multiplication of a vector v with the matrix A = sin ® cos 0 yields a vector p=Av which is a counter clockwise rotation of v by an angle of e. a) Find the vector p that is obtained if v = is rotated counter clockwise by 40°. b) Find the vector q that is obtained if v = is rotated clockwise by 40°.
Find a value of b so that 15i - 3j and -4i + bj are orthogonal.
Please solve and answer in the same format as the question as it makes it easier to follow. Box answers and do not type it out and I will give you a thumbs up rating if answered correctly. Chapter 3.4 Question 1
coordinate frame are given by aij The components of a first and second order tensor in a particular [2 1 61 = 3 0 3 b= = 1 2 4] Determine the components of each tensor in a new coordinate system found through a rotation of π/6 radians about the x3-axis. Choose a counterclockwise rotation when viewing down the negative x3-axis.

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The rotation matrix R= rotate the vector v = O [1 2] O O O K2 27 [cos (0) -sin (0) sin (0) cos (8) by an angle of when multiplied to a vector , rotates counter-clockwise by an angle. With this information, we want to in the CLOCKWISE direction. The rotated vector is