Prove for generic vectors u, v, w in R3 and c, d each vector property can be reduced to proper should all be relatively short. Some will be very a. ủ + ở = ở + ỉ b. (ū + v) + w = ỉ + (ở + w) c. c(u + ở) = cũ + cỏ (c + d)i – cỉ + diỉ %3D -

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 40E
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Prove for generic vectors ū, v, w in R³ and c, d in R the algebraic properties of vectors. [Hint:
each vector property can be reduced to properties of real numbers and definitions. These
should all be relatively short. Some will be very short.]
ủ + ở = ở + ủ
b. (ũ + ở) + w = ủ + (ở + w)
с. с(й + ) %3 сӣ + сі
а.
%3D
Transcribed Image Text:Prove for generic vectors ū, v, w in R³ and c, d in R the algebraic properties of vectors. [Hint: each vector property can be reduced to properties of real numbers and definitions. These should all be relatively short. Some will be very short.] ủ + ở = ở + ủ b. (ũ + ở) + w = ủ + (ở + w) с. с(й + ) %3 сӣ + сі а. %3D
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