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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 & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.1: Rectangular Coordinate Systems
Problem 7E
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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
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