(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).
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
Problem 38EQ
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