VAM_60-64

VAM_60-64 - Tutorial V AM: V ector Algebra and an...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Tutorial V AM: V ector Algebra and an Introduction to Matrices Exercise 62. a. In a rotation about the x-axis, only the y and z components are changed. Thus, the y-axis is turned toward the z-axis, and so forth. So, 0 1 1 0 0 R1 ('1) = @ 0 cos '1 sin '1 A : 0 sin '1 cos '1 b. In a right-handed rotation about the y-axis, the z-axis is turned toward the x-axis and the x-axis is turned toward the negative z-axis. Thus, 0 1 cos '2 0 sin '2 R2 ('2) = @ 0 1 0 A: sin '1 0 cos '1 Note that the negative sign follows the sin ' cyclically, not in terms of relative position within the matrix, i.e., it is not always on the upper row. c. In a right-handed rotation about the z-axis, the x-axis is turned toward the y-axis, etc. Thus, 0 1 cos '3 sin '3 0 cos '3 0 A : R3 ('3) = @ sin '3 0 0 1 Exercise 63. E(; ; ) = E3 ()E1()E3 () 0 10 10 1 cos sin 0 1 0 0 cos sin 0 cos sin A @ sin cos 0 A = @ sin cos 0 A @ 0 0 0 1 0 sin cos 0 0 1 0 1 cos cos sin cos sin cos sin + sin cos cos sin sin = @ sin cos cos cos sin sin sin + cos cos cos cos sin A : sin sin sin cos cos Exercise 64. RE (0; 0; 0) 0 10 10 1 cos 0 sin 0 0 1 0 0 cos 0 sin 0 0 = @ sin 0 cos 0 0 A @ 0 cos 0 sin 0 A @ sin 0 cos 0 0 A 0 0 1 0 sin 0 cos 0 0 0 1 53 Tutorial V AM: V ector Algebra and an Introduction to Matrices 1 cos 0 cos 0 sin 0 cos 0 sin 0 cos 0 sin 0 sin 0 cos 0 cos 0 sin 0 sin 0 = @ sin 0 cos 0 + cos 0 cos 0 sin 0 sin 0 sin 0 + cos 0 cos 0 cos 0 cos 0 sin 0 A : sin 0 sin 0 sin 0 cos 0 cos 0 0 54 ...
View Full Document

Page1 / 2

VAM_60-64 - Tutorial V AM: V ector Algebra and an...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online