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. Let A be a circle lying on the unit sphere S. Then there is a unique plane P in R³ such that PnS A. Recall from analytic geometry that P = {(x1, x2, x3): x1B₁ + x2ß₂ + x3/3 = l} where (B₁, B2, B3) is a vector orthogonal to P and is some real number. It can be assumed that 3²+32 +33 = 1. Use this information to show that if A contains the north pole N then its stereographic projection on C is a straight line. Otherwise, A projects onto a circle in C.

. Let A be a circle lying on the unit sphere S. Then there is a unique plane P in R³ such that PnS A. Recall from analytic geometry that P = {(x1, x2, x3): x1B₁ + x2ß₂ + x3/3 = l} where (B₁, B2, B3) is a vector orthogonal to P and is some real number. It can be assumed that 3²+32 +33 = 1. Use this information to show that if A contains the north pole N then its stereographic projection on C is a straight line. Otherwise, A projects onto a circle in C.

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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. Let A be a circle lying on the unit sphere S. Then there is a unique plane P in R³ such that PnS A. Recall from analytic geometry that P = {(x1, x2, x3): x1B₁ + x2ß2 + x3/3 = l} where (B1, B2, B3) is a vector orthogonal to P and is some real number. It can be assumed that 3²+32 +33 = 1. Use this information to show that if A contains the north pole N then its stereographic projection on C is a straight line. Otherwise, A projects onto a circle in C.
Transcribed Image Text:. Let A be a circle lying on the unit sphere S. Then there is a unique plane P in R³ such that PnS A. Recall from analytic geometry that P = {(x1, x2, x3): x1B₁ + x2ß2 + x3/3 = l} where (B1, B2, B3) is a vector orthogonal to P and is some real number. It can be assumed that 3²+32 +33 = 1. Use this information to show that if A contains the north pole N then its stereographic projection on C is a straight line. Otherwise, A projects onto a circle in C.
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