VAM_60-64

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

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

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