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Vectors Additional concepts found in the study of vectors include dot product (also called inner product) and cross product. Note: Some texts will use the vector "arrow" above the u and v and some do not. In the examples and problems you will see both methods used and the u and v will always denote vectors. k is a scalar. The dot product of two vectors u = and v= is denoted u v = ac + bd. In other words, the dot product of two vectors is the sum of the product of their first components and the product of their second components. 1. Show the following properties are true. Be sure to state your vectors before you show the property is true (example: u = ) u.v=v.u u. (v+w) = u v+u w ku v = k(u.v) = u. (kv) u. u = /u 1²

Vectors Additional concepts found in the study of vectors include dot product (also called inner product) and cross product. Note: Some texts will use the vector "arrow" above the u and v and some do not. In the examples and problems you will see both methods used and the u and v will always denote vectors. k is a scalar. The dot product of two vectors u = and v= is denoted u v = ac + bd. In other words, the dot product of two vectors is the sum of the product of their first components and the product of their second components. 1. Show the following properties are true. Be sure to state your vectors before you show the property is true (example: u = ) u.v=v.u u. (v+w) = u v+u w ku v = k(u.v) = u. (kv) u. u = /u 1²

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Vectors Additional concepts found in the study of vectors include dot product (also called inner product) and cross product. Note: Some texts will use the vector "arrow" above the u and v and some do not. In the examples and problems you will see both methods used and the u and v will always denote vectors. k is a scalar. ● The dot product of two vectors u = <a, b> and v= < c, d> is denoted u vac + bd. In other words, the dot product of two vectors is the sum of the product of their first components and the product of their second components. 1. Show the following properties are true. Be sure to state your vectors before you show the property is true (example: u = <a, b>) u. V = v. U u. (v + w) = u v+u w 6 ku v = k(u.v) = u. (kv) ● u₁u = |u₁|²
Transcribed Image Text:Vectors Additional concepts found in the study of vectors include dot product (also called inner product) and cross product. Note: Some texts will use the vector "arrow" above the u and v and some do not. In the examples and problems you will see both methods used and the u and v will always denote vectors. k is a scalar. ● The dot product of two vectors u = <a, b> and v= < c, d> is denoted u vac + bd. In other words, the dot product of two vectors is the sum of the product of their first components and the product of their second components. 1. Show the following properties are true. Be sure to state your vectors before you show the property is true (example: u = <a, b>) u. V = v. U u. (v + w) = u v+u w 6 ku v = k(u.v) = u. (kv) ● u₁u = |u₁|²
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