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Find parametric equations for the line. (Use the parameter t.) The line through the points (0,, 1) and (9, 1, –4) (x(t), y(t), z(t)) = Find the symmetric equations. x – 9 2 = 2y - 2 = 2+ 4 -5 z + 4 -5 2x - 2 = Y-2 = x +4 = 2y - 2 =5 -5 9 + 9x = 1 + Y = -4 - %3D 5z Ox- 9 = 2y - 2 = z + 4

Find parametric equations for the line. (Use the parameter t.) The line through the points (0,, 1) and (9, 1, –4) (x(t), y(t), z(t)) = Find the symmetric equations. x – 9 2 = 2y - 2 = 2+ 4 -5 z + 4 -5 2x - 2 = Y-2 = x +4 = 2y - 2 =5 -5 9 + 9x = 1 + Y = -4 - %3D 5z Ox- 9 = 2y - 2 = z + 4

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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**Find Parametric and Symmetric Equations for a Line** This section will guide you through finding both parametric and symmetric equations for a line given two points in 3D space. ### Problem Statement **Find parametric equations for the line. (Use the parameter \( t \).)** Given points: \[ \left( 0, \frac{1}{2}, 1 \right) \] \[ \left( 9, 1, -4 \right) \] The parametric form of the line is: \[ (x(t), y(t), z(t)) = ( \_\_\_ \times t ) \] ### Parametric Equations Solution In this part, the parametric form of the equation hasn't been fully solved and is left incomplete, indicated by the empty parentheses. ### Finding the Symmetric Equations To find the symmetric equations, we solve for each variable \( (x, y, z) \) in terms of a common parameter based on the given points. We have the following options: 1. \( \frac{x - 9}{9} = \frac{2y - 2}{-\frac{1}{2}} = \frac{z + 4}{-5} \) 2. \( 2x - 2 = \frac{y - \frac{9}{9}}{z + \frac{4}{-5}} \) 3. \( \frac{x + 4}{-\frac{5}{2}} = 2y - 2 = \frac{z - \frac{9}{9}}{z - 9} \) 4. \( 9 + 9x = 1 + \frac{y}{2} = -4 - 5z \) 5. \( x - 9 = 2y - 2 = z + 4 \) ### Correct Symmetric Equations The correct symmetric equations are: \[ \frac{x - 9}{9} = \frac{2y - 2}{1} = \frac{z + 4}{-5} \] This option is boxed and marked with a checkbox, indicating it as the correct answer. ### Explanation From the given points, the direction vector \(\mathbf{d}\) can be determined: \[ \mathbf{d} = (9 - 0, 1 - \frac{1}{2}, -4
Transcribed Image Text:**Find Parametric and Symmetric Equations for a Line** This section will guide you through finding both parametric and symmetric equations for a line given two points in 3D space. ### Problem Statement **Find parametric equations for the line. (Use the parameter \( t \).)** Given points: \[ \left( 0, \frac{1}{2}, 1 \right) \] \[ \left( 9, 1, -4 \right) \] The parametric form of the line is: \[ (x(t), y(t), z(t)) = ( \_\_\_ \times t ) \] ### Parametric Equations Solution In this part, the parametric form of the equation hasn't been fully solved and is left incomplete, indicated by the empty parentheses. ### Finding the Symmetric Equations To find the symmetric equations, we solve for each variable \( (x, y, z) \) in terms of a common parameter based on the given points. We have the following options: 1. \( \frac{x - 9}{9} = \frac{2y - 2}{-\frac{1}{2}} = \frac{z + 4}{-5} \) 2. \( 2x - 2 = \frac{y - \frac{9}{9}}{z + \frac{4}{-5}} \) 3. \( \frac{x + 4}{-\frac{5}{2}} = 2y - 2 = \frac{z - \frac{9}{9}}{z - 9} \) 4. \( 9 + 9x = 1 + \frac{y}{2} = -4 - 5z \) 5. \( x - 9 = 2y - 2 = z + 4 \) ### Correct Symmetric Equations The correct symmetric equations are: \[ \frac{x - 9}{9} = \frac{2y - 2}{1} = \frac{z + 4}{-5} \] This option is boxed and marked with a checkbox, indicating it as the correct answer. ### Explanation From the given points, the direction vector \(\mathbf{d}\) can be determined: \[ \mathbf{d} = (9 - 0, 1 - \frac{1}{2}, -4
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