Find the projective line h through u and v with u = (1,2, –3) and v = (-1,0, –1); also find the projective line k through w = (0, 1, 2) and z = (1, –1,1). Find the intersection point of the lines h and k in part (a). Consider the four points A, B, C, D in the projective plane with A(2,1,0), B(5, 4, – 1), C(1,5, –3) and D(1,2, – 1). Show that the four points A, B,C, D are collinear and find the cross ratio R(A, D;C,B).
Find the projective line h through u and v with u = (1,2, –3) and v = (-1,0, –1); also find the projective line k through w = (0, 1, 2) and z = (1, –1,1). Find the intersection point of the lines h and k in part (a). Consider the four points A, B, C, D in the projective plane with A(2,1,0), B(5, 4, – 1), C(1,5, –3) and D(1,2, – 1). Show that the four points A, B,C, D are collinear and find the cross ratio R(A, D;C,B).
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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Transcribed Image Text:2. (a) :
find the projective line k through w =
Find the projective line h through u and v with u = (1, 2, –3) and v = (–-1,0, –1); also
(0,1, 2) and z = (1, –1,1).
(b)
Find the intersection point of the lines h and k in part (a).
(c)
C(1,5, –3) and D(1,2, –1).
Show that the four points A, B, C, D are collinear and find the cross ratio R(A, D;C, B).
Consider the four points A, B, C, D in the projective plane with A(2, 1,0), B(5, 4, –1),
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