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Algebra Linear - Demonstrating Orthogonality of Linear Equations and Vector Directions, Essays (university) of Computer Networks
A university assignment submitted by student viviana andrea cardona guzmán, with code 1.007.329.801, for the algebra linear course under the program of administración de empresas at universidad nacional abierta y a distancia unad. The assignment involves demonstrating the orthogonality of the given linear equations and their vector directions. The equations are presented in matrix form and the vectors of direction are calculated and their orthogonality is proven by calculating their cross product.
What you will learn
- How to calculate the vectors of direction for given linear equations?
- What is the meaning of orthogonality in linear algebra?
- How to prove the orthogonality of two vectors using their cross product?
Typology: Essays (university)
2019/2020
1 / 2
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Unidad 2: Tarea 2 - Sistemas de ecuaciones lineales, rectas, planos y espacios vectoriales Grupo: 100408_
Presentado por estudiante Viviana Andrea Cardona Guzmán _ Código: 1.007.329.
Presentado a Tutor Gonzalo Fester
Universidad Nacional Abierta y a Distancia UNAD Escuela de Ciencias Administrativas, Contables, Económicas y de Negocios Programa: Administración De Empresas Curso: Algebra Lineal _ 100408 La Dorada Caldas 05-Abril-
Ejercicio 3
b) Demostrar si las rectas 𝑥−3 12 = 𝑦−3 16 = 7−𝑧 16 y 𝑥+2 12 = 5−𝑦−16 = 𝑧+6−
𝑥−3 12 = 𝑦−3 16 = 7−𝑧 16 𝑥+2 12 = 5−𝑦−16 = 𝑧+6−
Los vectores de dirección de las rectas son:
𝑉 1 = 12𝑖 + 16𝑗 − 16𝑘
𝑉 2 = 12𝑖 + 16𝑗 − 16𝑘
El producto 𝑉 1 y 𝑉 2 : Hacemos que el producto cruz demostrar que son ortogonales.
𝑉 1 = 𝑋 = 3 + 12 𝑌 = 3 + 16 𝑍 = 7 − 16
𝑉 2 = 𝑋 = −2 + 12 𝑌 = 5 + 16 𝑍 = −6 − 16
Hacemos el producto Cruz
𝐴 1 = [𝑖 𝑗 𝑘 12 16 − 16 12 + 16 − 16 ] = 𝑖|16 − 16 16 − 16 | = 𝑗 |12 − 16 12 − 16 | = 𝑘 |12 16 12 + 16 | 𝑨 = 𝟎𝒊 − 𝟎𝒋 + 𝟎𝒌 = 𝟎 𝑶𝒓𝒕𝒐𝒈𝒂𝒍𝒆𝒔