Three points with position vectors a, b, and c will be collinear (lie on a line) if the parallelogram with adja- cent sides a -b and a -c has zero geometrical area. Use this result in Exercises 25 through 28 to determine which sets of points are collinear. 25. (2, 2, 3), (6, 1,5), (-2, 4, 3).

Three points with position vectors a, b, and c will be collinear (lie on a line) if the parallelogram with adja- cent sides a -b and a -c has zero geometrical area. Use this result in Exercises 25 through 28 to determine which sets of points are collinear. 25. (2, 2, 3), (6, 1,5), (-2, 4, 3).

Elementary Geometry For College Students, 7e

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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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Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.

Question

Three points with position vectors a, b, and e will be
collinear (lie on a line) if the parallelogram with adja-
cent sides a - b and a -c has zero geometrical area.
Use this result in Exercises 25 through 28 to determine
which sets of points are collinear.
25. (2, 2, 3), (6, 1,5). (-2, 4, 3).

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