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Find sets of parametric equations and symmetric equations of the line that passes through the given point and is parallel to the given vector or line. (For each line, write the direction numbers as integers.) Point Parallel to (-5, 0, 9) v = 4i + 5j - 7k (a) parametric equations (Enter your answers as a comma-separated list.) (b) symmetric equations O 4x = - = 72

Find sets of parametric equations and symmetric equations of the line that passes through the given point and is parallel to the given vector or line. (For each line, write the direction numbers as integers.) Point Parallel to (-5, 0, 9) v = 4i + 5j - 7k (a) parametric equations (Enter your answers as a comma-separated list.) (b) symmetric equations O 4x = - = 72

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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### Finding Parametric and Symmetric Equations of a Line This example demonstrates how to find sets of parametric and symmetric equations for a line passing through a given point and parallel to a given vector or line. The equations use integer direction numbers. #### Given: - **Point:** (-5, 0, 9) - **Parallel to the vector:** **v** = 4i + 5j - 7k #### Task: 1. Find the parametric equations. - (Enter your answers as a comma-separated list in the provided box.) 2. Find the symmetric equations. - Options are given in mathematical form. #### Solutions: ##### (a) Parametric Equations Find the parametric equations for the line. Enter your answers as a comma-separated list in the provided box. ##### (b) Symmetric Equations Select the correct symmetric equations from the given options: - \(4x = \frac{y}{5} = 7z\) - \(\frac{x - 5}{4} = y = \frac{z}{7}\) - \(\frac{x + 5}{4} = \frac{y}{5} = \frac{9 - z}{7}\) - \(\frac{x}{4} = \frac{y}{5} = \frac{z}{7}\) Each option provides a different relationship between x, y, and z for the line defined by the given point and parallel vector.
Transcribed Image Text:### Finding Parametric and Symmetric Equations of a Line This example demonstrates how to find sets of parametric and symmetric equations for a line passing through a given point and parallel to a given vector or line. The equations use integer direction numbers. #### Given: - **Point:** (-5, 0, 9) - **Parallel to the vector:** **v** = 4i + 5j - 7k #### Task: 1. Find the parametric equations. - (Enter your answers as a comma-separated list in the provided box.) 2. Find the symmetric equations. - Options are given in mathematical form. #### Solutions: ##### (a) Parametric Equations Find the parametric equations for the line. Enter your answers as a comma-separated list in the provided box. ##### (b) Symmetric Equations Select the correct symmetric equations from the given options: - \(4x = \frac{y}{5} = 7z\) - \(\frac{x - 5}{4} = y = \frac{z}{7}\) - \(\frac{x + 5}{4} = \frac{y}{5} = \frac{9 - z}{7}\) - \(\frac{x}{4} = \frac{y}{5} = \frac{z}{7}\) Each option provides a different relationship between x, y, and z for the line defined by the given point and parallel vector.
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