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Find an equation of the plane passing through the three points: (1, -2, 1), (-1, -1, 7), (2, -1, 3).

Find an equation of the plane passing through the three points: (1, -2, 1), (-1, -1, 7), (2, -1, 3).

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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Find an equation of the plane passing through the three points: (1, -2, 1), (-1, -1, 7), (2, -1, 3).

1. Use Cramer's Rule to solve the system of linear equations, if possible. 7x3 = -21 2 14x₁ - 21x₂ - 7x3 21x₂ - - 4x₁ + 2x₂ - 2x3 = 56x₁ - 21x₂ + 7x3 = 7 2. Find the area of the triangle having the given vertices: (-1, 2), (2, 2), (-2, 4). 3. Find the volume of the tetrahedron having the given vertices: (1, 0, 0), (0, 1, 0), (0, 0, 1). (1. 1. 4. Find an equation of the plane passing through the three points: (1, -2, 1), (-1, -1, 7), (2, -1, 3).
Transcribed Image Text:1. Use Cramer's Rule to solve the system of linear equations, if possible. 7x3 = -21 2 14x₁ - 21x₂ - 7x3 21x₂ - - 4x₁ + 2x₂ - 2x3 = 56x₁ - 21x₂ + 7x3 = 7 2. Find the area of the triangle having the given vertices: (-1, 2), (2, 2), (-2, 4). 3. Find the volume of the tetrahedron having the given vertices: (1, 0, 0), (0, 1, 0), (0, 0, 1). (1. 1. 4. Find an equation of the plane passing through the three points: (1, -2, 1), (-1, -1, 7), (2, -1, 3).
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