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(a) Specify the Euler angle rotation matrices Rx, Ry and Rz for rotation about the X, Y and Z-axis respectively. (b) Give the homogeneous transformation matrix T for an anticlockwise rotation of 30 degrees about the Y-axis followed by a translation of (-1,2,5) (c) Evaluate the transformation of the point p=(4,5,6) and the vector v=(3,-1,2) by the transformation matrix T defined in part 1(b), giving the answer in homogeneous and Euclidean coordinates. (d) Evaluate the unit normal and area of triangle t with vertices p1=(4,5,6), p2=(1,0,0) and p3=(2,6,7).

(a) Specify the Euler angle rotation matrices Rx, Ry and Rz for rotation about the X, Y and Z-axis respectively. (b) Give the homogeneous transformation matrix T for an anticlockwise rotation of 30 degrees about the Y-axis followed by a translation of (-1,2,5) (c) Evaluate the transformation of the point p=(4,5,6) and the vector v=(3,-1,2) by the transformation matrix T defined in part 1(b), giving the answer in homogeneous and Euclidean coordinates. (d) Evaluate the unit normal and area of triangle t with vertices p1=(4,5,6), p2=(1,0,0) and p3=(2,6,7).

Advanced Engineering Mathematics
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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(a) Specify the Euler angle rotation matrices Rx, Ry and Rz for rotation about the X, Y and Z-axis respectively. (b) Give the homogeneous transformation matrix T for an anticlockwise rotation of 30 degrees about the Y-axis followed by a translation of (-1,2,5) (c) Evaluate the transformation of the point p=(4,5,6) and the vector v=(3,-1,2) by the transformation matrix T defined in part 1(b), giving the answer in homogeneous and Euclidean coordinates. (d) Evaluate the unit normal and area of triangle t with vertices p1=(4,5,6), p2=(1,0,0) and p3=(2,6,7).
Transcribed Image Text:(a) Specify the Euler angle rotation matrices Rx, Ry and Rz for rotation about the X, Y and Z-axis respectively. (b) Give the homogeneous transformation matrix T for an anticlockwise rotation of 30 degrees about the Y-axis followed by a translation of (-1,2,5) (c) Evaluate the transformation of the point p=(4,5,6) and the vector v=(3,-1,2) by the transformation matrix T defined in part 1(b), giving the answer in homogeneous and Euclidean coordinates. (d) Evaluate the unit normal and area of triangle t with vertices p1=(4,5,6), p2=(1,0,0) and p3=(2,6,7).
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