Question 2: (25 points) (3D rotations) Three points P, P2 and P3 are given. Pi is...

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Question 2: (25 points) (3D rotations) Three points P₁, P2 and P3 are given. Pi is at (10, 15, 20). Point P2 is at (10+cos0, 15-sin0, 20). Point P3 is at (10+sinė, 15+cose, 20). Here is arbitrary. (1)(15 points) Transform the points so that point Pi is at the origin, P2 lies on the positive x-axis, and P3 lies on the positive y-axis. (ii) (5 point) Explain why your transformation would work? (iii) (5 points) Calculate the new location of point P2 and P3 after the transformation using the transformation developed. Show all your work. Standard 2Drotation matrices are given below. 3D matrices can be also found in our textbook. cos Ray(0)= sine 0 sin 0 Cos 0 0 0 R₁2 (0) = = 0 0 0 cos 0 sin 0 - sin 0 and cos 6 R₂(0): cos 0 sin 0] 01 0 sin 0 cos = - [ Question 2: (25 points) (3D rotations) Three points P₁, P2 and P3 are given. Pi is at (10, 15, 20). Point P2 is at (10+cos0, 15-sin0, 20). Point P3 is at (10+sinė, 15+cose, 20). Here is arbitrary. (1)(15 points) Transform the points so that point Pi is at the origin, P2 lies on the positive x-axis, and P3 lies on the positive y-axis. (ii) (5 point) Explain why your transformation would work? (iii) (5 points) Calculate the new location of point P2 and P3 after the transformation using the transformation developed. Show all your work. Standard 2Drotation matrices are given below. 3D matrices can be also found in our textbook. cos Ray(0)= sine 0 sin 0 Cos 0 0 0 R₁2 (0) = = 0 0 0 cos 0 sin 0 - sin 0 and cos 6 R₂(0): cos 0 sin 0] 01 0 sin 0 cos = - [

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i15 points Transform the points so that point P1 is at the origin P2 lies on the positive xaxis and P3 lies on the positive yaxis To achieve this we c... View the full answer