Homework Help is Here – Start Your Trial Now!
Math
Algebra
1. Proof the remaining Dot product properties Let a = (1,2, –3), b = (0, 2, 4), and c = (5, –1,3). Find each of the following products. a. (a · b)c b. а (2с) c. ||b||²

1. Proof the remaining Dot product properties Let a = (1,2, –3), b = (0, 2, 4), and c = (5, –1,3). Find each of the following products. a. (a · b)c b. а (2с) c. ||b||²

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
See similar textbooks
Question
Answer number 1
Dot product Proof Let u = (u1, u2, u3) and v = (v1, v2, V3). Then u v = (u1, u2, u3) · (v1, v2, V3) = u1 v1 + uz v2+u3 V3 = vịu1 + v2u2 + v3U3 = (v1, v2 , V3) · (u1 , u2, u3) = v. u. c(u. v) = c(u vị +u2v2 +u3v3) = c(u,v1)+c(uzva)+c(uzv3) = (cui )v1 + (cu2)v2 + (cu3)v3 = (cu1, cu2, cu3) · (v1, v2, V3) = c{u, uz, us) · (v1, v2, v3) = (cu) - v. Dot product Exercises 1. Proof the remaining Dot product properties Let a = (1,2, –3), b = (0, 2,4), and ĉ = (5, –1,3). Find each of the following products. а. (а Б)с b. a · (2c) c. ||b||2 Dot product Using the Dot Product to Find the Angle between Two Vectors When two nonzero vectors are placed in standard position, whether in two dimensions or three dimen between them (Figure 11.3.1). The dot product provides a way to find the measure of this angle. This fact that we can express the dot product in terms of the cosine of the angle formed by two vectors. Figure 11.3.1: Let 0 be the angle between two nonzero vectors ū and v such that 0 <0
Transcribed Image Text:Dot product Proof Let u = (u1, u2, u3) and v = (v1, v2, V3). Then u v = (u1, u2, u3) · (v1, v2, V3) = u1 v1 + uz v2+u3 V3 = vịu1 + v2u2 + v3U3 = (v1, v2 , V3) · (u1 , u2, u3) = v. u. c(u. v) = c(u vị +u2v2 +u3v3) = c(u,v1)+c(uzva)+c(uzv3) = (cui )v1 + (cu2)v2 + (cu3)v3 = (cu1, cu2, cu3) · (v1, v2, V3) = c{u, uz, us) · (v1, v2, v3) = (cu) - v. Dot product Exercises 1. Proof the remaining Dot product properties Let a = (1,2, –3), b = (0, 2,4), and ĉ = (5, –1,3). Find each of the following products. а. (а Б)с b. a · (2c) c. ||b||2 Dot product Using the Dot Product to Find the Angle between Two Vectors When two nonzero vectors are placed in standard position, whether in two dimensions or three dimen between them (Figure 11.3.1). The dot product provides a way to find the measure of this angle. This fact that we can express the dot product in terms of the cosine of the angle formed by two vectors. Figure 11.3.1: Let 0 be the angle between two nonzero vectors ū and v such that 0 <0
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS