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Find an equation of the plane passing through the given points (2, 9, –9), (2, –9, 9), (-2, –9, –9)

Find an equation of the plane passing through the given points (2, 9, –9), (2, –9, 9), (-2, –9, –9)

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 an equation of the plane passing through the given points. **Given Points**: \((2, 9, -9)\), \((2, -9, 9)\), \((-2, -9, -9)\) **Diagram Description**: There is a blank rectangular box, presumably for the answer or calculations.
Transcribed Image Text:**Problem Statement**: Find an equation of the plane passing through the given points. **Given Points**: \((2, 9, -9)\), \((2, -9, 9)\), \((-2, -9, -9)\) **Diagram Description**: There is a blank rectangular box, presumably for the answer or calculations.
**Determine whether Cramer's Rule is used correctly to solve for the variable. If not, identify the mistake.** \[ \begin{aligned} x + 3y + z &= 3 \\ -x + 4y - 3z &= 2 \\ 2x + y - z &= 6 \\ \end{aligned} \] \[ y = \frac{\begin{vmatrix} 1 & \textcolor{red}{3} & 1 \\ -1 & 4 & -3 \\ 2 & 1 & -1 \end{vmatrix}}{\begin{vmatrix} 1 & \textcolor{red}{3} & 1 \\ -1 & \textcolor{red}{2} & -3 \\ 2 & \textcolor{red}{6} & -1 \end{vmatrix}} \] - **Option A**: The numerator and denominator have been reversed. The determinant of the coefficient matrix should be in the denominator. - **Option B**: The row of constants should be in the second row. - **Option C**: There is no mistake. - **Option D**: The column of constants should be in the first column. - **Option E**: The numerator and denominator have been reversed. The determinant of the coefficient matrix should be in the numerator.
Transcribed Image Text:**Determine whether Cramer's Rule is used correctly to solve for the variable. If not, identify the mistake.** \[ \begin{aligned} x + 3y + z &= 3 \\ -x + 4y - 3z &= 2 \\ 2x + y - z &= 6 \\ \end{aligned} \] \[ y = \frac{\begin{vmatrix} 1 & \textcolor{red}{3} & 1 \\ -1 & 4 & -3 \\ 2 & 1 & -1 \end{vmatrix}}{\begin{vmatrix} 1 & \textcolor{red}{3} & 1 \\ -1 & \textcolor{red}{2} & -3 \\ 2 & \textcolor{red}{6} & -1 \end{vmatrix}} \] - **Option A**: The numerator and denominator have been reversed. The determinant of the coefficient matrix should be in the denominator. - **Option B**: The row of constants should be in the second row. - **Option C**: There is no mistake. - **Option D**: The column of constants should be in the first column. - **Option E**: The numerator and denominator have been reversed. The determinant of the coefficient matrix should be in the numerator.
Expert Solution
Step 1

(A) To find the equation of plane passing through below points.

2,9,−9, 2,−9,9, −2,−9,−9

 

(B) To determine the correct statement.

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