Homework 3 Solution

1 the precise denition of the plcker coordinate p l u

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: :Z :W ) . (1) The precise definition of the Pl¨cker coordinate P l ℓ u 5 in P (P0 :P1 :P2 :P3 :P4 :P5 ) is Pl ℓ = of ℓ as a point cd bd bc ad ac a 1 b1 : 11: 11: 11: 11: 11 c2 d2 b 2 d2 b2 c2 a 2 d2 a2 c2 a 2 b2 . • See “Review of Lectures – XIII”, page 1, Definition. (2) True or false : “P l ℓ does not depend on a1 , b1 , c1 d1 , a2 , b2 , c2 , d2 , but depends only on ℓ.” • The answer is true . See “Review of Lectures – XIII”, page 2, Proposition A. (3) If your answer in (2) is ‘false’, then give a concrete example of a pair of systems both of which are of the form (#) that define the same line yet designate two distinct points in P5 (P0 :P1 :P2 :P3 :P4 :P5 ) . If not applicable, then simply say “not applicable”. • The answer is not applicable . (4) True or false : “Suppose (#) a1 X + b1 Y + c1 Z + d1 W = 0, a2 X + b2 Y + c2 Z + d2 W = 0 defines a line ℓ ⊆ P3 (X :Y :Z :W ) , and 2 (#)′ a1 ′ X + b1 ′ Y + c1 ′ Z + d1 ′ W = 0, a...
View Full Document

This note was uploaded on 11/06/2013 for the course MATH 660 taught by Professor Yasuyukikachi during the Fall '13 term at Kansas.

Ask a homework question - tutors are online