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This question is about about quaternions and the use of quaternions to represent 3D rotations: (a) For each of the fundamental unit quaternions i, j, k, state the angle and aris of the rotation they represent. (b) If r = zi + wj + zk is any pure quaternion, what can you say about each of it/i, jv/j, kr/k? (e) Prove, by induction on n, that for all n, a product of n fundamental unit quaternions represents a rotation by either 0° (in which case it does nothing) or 180°. ART A , B

This question is about about quaternions and the use of quaternions to represent 3D rotations: (a) For each of the fundamental unit quaternions i, j, k, state the angle and aris of the rotation they represent. (b) If r = zi + wj + zk is any pure quaternion, what can you say about each of it/i, jv/j, kr/k? (e) Prove, by induction on n, that for all n, a product of n fundamental unit quaternions represents a rotation by either 0° (in which case it does nothing) or 180°. ART A , B

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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This question is about about quaternions and the use of quaternions to represent 3D rotations: (a) For each of the fundamental unit quaternions i, j, k, state the angle and aris of the rotation they represent. (b) If v = ri + vj + zk is any pure quaternion, what can you say about each of iv/i, ju/j, ku/k? (c) Prove, by induction on n, that for all n, a product of n fundamental unit quaternions represents a rotation by either 0° (in which case it does nothing) or 180°. PART A, B
Transcribed Image Text:This question is about about quaternions and the use of quaternions to represent 3D rotations: (a) For each of the fundamental unit quaternions i, j, k, state the angle and aris of the rotation they represent. (b) If v = ri + vj + zk is any pure quaternion, what can you say about each of iv/i, ju/j, ku/k? (c) Prove, by induction on n, that for all n, a product of n fundamental unit quaternions represents a rotation by either 0° (in which case it does nothing) or 180°. PART A, B
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