Let ~u = ( 1, -1, 0) and ~v = ( -1, 0, 1). Find ~u - ~v and ~u + ~v. b) Are the vectors ~u − ~v and ~u + ~v orthogonal. (c) Explain in general that, given any two vectors ~w1 and ~w2, ~w1 − ~w2 and ~w1 + ~w2 are orthogonal if || ~w1|| = || ~w2

Let ~u = ( 1, -1, 0) and ~v = ( -1, 0, 1). Find ~u - ~v and ~u + ~v. b) Are the vectors ~u − ~v and ~u + ~v orthogonal. (c) Explain in general that, given any two vectors ~w1 and ~w2, ~w1 − ~w2 and ~w1 + ~w2 are orthogonal if || ~w1|| = || ~w2

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

a) Let ~u = ( 1, -1, 0) and ~v = ( -1, 0, 1). Find ~u - ~v and ~u + ~v.

b) Are the vectors ~u − ~v and ~u + ~v orthogonal.

(c) Explain in general that, given any two vectors ~w1 and ~w2, ~w1 − ~w2 and ~w1 + ~w2 are orthogonal if || ~w1|| = || ~w2||.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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