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Unformatted text preview: :Z :W ) .
The precise deﬁnition of the Pl¨cker coordinate P l ℓ
in P (P0 :P1 :P2 :P3 :P4 :P5 ) is
Pl ℓ = of ℓ as a point cd
a 1 b1
: 11: 11: 11: 11: 11
b 2 d2
a 2 d2
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
• The answer is not applicable .
(4) True or false :
(#) 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,
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This note was uploaded on 11/06/2013 for the course MATH 660 taught by Professor Yasuyukikachi during the Fall '13 term at Kansas.
- Fall '13