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For each statement, determine whether it true or false, and justify your answer. a) In R³ if two lines are not parallel, they must intersect at a point. b) For u, v, w in R", if u +w=+w then u = v. c) There are no vectors u and 7 in R" such that ||ū|| = 1, ||v|| = 3, and ū - v = 6.

For each statement, determine whether it true or false, and justify your answer. a) In R³ if two lines are not parallel, they must intersect at a point. b) For u, v, w in R", if u +w=+w then u = v. c) There are no vectors u and 7 in R" such that ||ū|| = 1, ||v|| = 3, and ū - v = 6.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter2: Parallel Lines
Section2.3: Proving Lines Parallel
Problem 34E
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For each statement, determine whether it is true or false, and justify your answer. a) In R³ if two lines are not parallel, they must intersect at a point. b) For u, v, w in R", if u +w=v+w then u = 7. V. c) There are no vectors u and 7 in R" such that |||| = 1, ||v|| = 3, and u · V = 6.
Transcribed Image Text:For each statement, determine whether it is true or false, and justify your answer. a) In R³ if two lines are not parallel, they must intersect at a point. b) For u, v, w in R", if u +w=v+w then u = 7. V. c) There are no vectors u and 7 in R" such that |||| = 1, ||v|| = 3, and u · V = 6.
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