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Find a set of parametric equations of the line with the given characteristics. (Enter your answers as a comma-separated list.) The line passes through the point (-3, 5, 9) and is perpendicular to the plane given by -x + 3y + z = 5.

Find a set of parametric equations of the line with the given characteristics. (Enter your answers as a comma-separated list.) The line passes through the point (-3, 5, 9) and is perpendicular to the plane given by -x + 3y + z = 5.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Problem Statement:** Find a set of parametric equations of the line with the given characteristics. (Enter your answers as a comma-separated list.) The line passes through the point \((-3, 5, 9)\) and is perpendicular to the plane given by \(-x + 3y + z = 5\). **Solution Explanation:** To find the parametric equations of a line, we need a point through which the line passes and a direction vector. Here, the line passes through the point \((-3, 5, 9)\). The line is perpendicular to the plane \(-x + 3y + z = 5\). The normal vector to the plane, which serves as the direction vector for the line, is \((-1, 3, 1)\). Using these, the parametric equations of the line can be written as: - \(x = -3 - t\) - \(y = 5 + 3t\) - \(z = 9 + t\) Here, \(t\) is a parameter that varies over all real numbers.
Transcribed Image Text:**Problem Statement:** Find a set of parametric equations of the line with the given characteristics. (Enter your answers as a comma-separated list.) The line passes through the point \((-3, 5, 9)\) and is perpendicular to the plane given by \(-x + 3y + z = 5\). **Solution Explanation:** To find the parametric equations of a line, we need a point through which the line passes and a direction vector. Here, the line passes through the point \((-3, 5, 9)\). The line is perpendicular to the plane \(-x + 3y + z = 5\). The normal vector to the plane, which serves as the direction vector for the line, is \((-1, 3, 1)\). Using these, the parametric equations of the line can be written as: - \(x = -3 - t\) - \(y = 5 + 3t\) - \(z = 9 + t\) Here, \(t\) is a parameter that varies over all real numbers.
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