8. For a fixed frame F with X, Y, and Z-axes, if frame A is obtained by rotating the axis Xfor angle, then the rotation matrix Qx can be described by ( )Z. ZA.B.[100 sin0 coscos -sinsin00cossin0cos 001B.D.0 sin010-sin 0 coscos1 00 cos0sin0sincos"XX"VFrame, AFrame, F

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Answered: 8. For a fixed frame F with X, Y, and…

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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Assignment 6 Problem 4 (Please answer it correctly): If r(t)=cos(3t)i+sin(3t)j+8tk
I I I I I I I I I I I I - Your answer is partially correct. Find parametric equations of the line through (-3,1 parallel to 4i-8j+ k. www ***** x(t) = 4t-3 y(t) = -8t+ z(t) = t + 6 k 18 X X
3) (a) Eliminate the parameter of the parametric equation x = 4 sin and y =1+ 2 cos (b) Write parametric equations describing the motion of a particle moving under uniform linear motion from point A(-3, 2) to point B(9, -6) in 4 sec.
9.45.) (a) Use the figure to show that x =r cos ø, y =r sin ø and x' = r cos( ø– 0),y' = r sin (4 –- 0). P(x, y) or P(x', y') FIGURE 7.4.6 Rotated axes in Problem 36 (b) Use the results from part (a) to derive the rotation equations: x' = x cos 0+ y sin 0 y' = -x sin 0 + y cos 0 (c) Use x' = x cos 0+ y sin 0 and y' = -x sin 0 + y cos 0 to find rotation equations in: x = x' cos 0 – y' sin 0 y = x' sin 0 – y' cos 0
16. Triangle CDE with vertices C(2, 4), D(6, 7), and E(7, 3): 90° counterclockwise about the origin C'(_ D'(__, E' (_,
4. Let ū = (2/3, 2), i = (-1, v3) (a) Find ū · v (b) Find |ū], || (c) If 0 is the angle between u and v, find cos 0. (d) Find 0. Answer: u · ở = 0; [ū| = 4, |ủ| = 2 ; cos 0=0; 0 = 90°
4. (a) What is the composition of a 90 degree rotation about the origin, followed by a 90 degree rotation about (1,0)? (b) What is the composition of a 90 degree rotation about the origin, followed by the reflection across the line x=y?

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8. For a fixed frame F with X, Y, and Z-axes, if frame A is obtained by rotating the axis X for angle, then the rotation matrix Qx can be described by ( ) A. B. [10 0 sin 0 cos cos-sin sin 0 cos 0 0 cos sin' 0 B. D. cos 0 sin 010 -sin 0 cos 0 0 cos 0 sin 0 -sin cos Z. Z. Frame, A Frame, F Y