Linear Algebra: A Modern Introduction

Published by Cengage Learning
ISBN 10: 1285463242
ISBN 13: 978-1-28546-324-7

Chapter 1 - Vectors - 1.3 Lines and Planes - Exercises 1.3 - Page 44: 3


Vector form:$\begin{bmatrix}{x \\y}\end{bmatrix} = \begin{bmatrix}{1 \\0}\end{bmatrix}+t\begin{bmatrix}{-1 \\3}\end{bmatrix}$; Parametric form is: $x=1-t, y=3t$

Work Step by Step

The vector form of a line is: $x=p+td$ This implies:$\begin{bmatrix}{x \\y}\end{bmatrix} = \begin{bmatrix}{1 \\0}\end{bmatrix}+t\begin{bmatrix}{-1 \\3}\end{bmatrix}$ And: Parametric equations of a line are defined as the equations which are correspond to the components of the vector. Thus, the parametric form of the equation of the line is: $x=1-t, y=3t$ Hence, the vector form is:$\begin{bmatrix}{x \\y}\end{bmatrix} = \begin{bmatrix}{1 \\0}\end{bmatrix}+t\begin{bmatrix}{-1 \\3}\end{bmatrix}$; Parametric form: $x=1-t, y=3t$
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