Find the distance d between the points P₁(7, 1, 10) and P₂(−3, 10, 3) by first finding the vector v from P₁ to P2, then finding the length of v. Use the square root symbol '√' where needed to give an exact value for your answer. V = d = 0
Find the distance d between the points P₁(7, 1, 10) and P₂(−3, 10, 3) by first finding the vector v from P₁ to P2, then finding the length of v. Use the square root symbol '√' where needed to give an exact value for your answer. V = d = 0
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 Description:**
Find the distance \( d \) between the points \( P_1(7, 1, 10) \) and \( P_2(-3, 10, 3) \) by first finding the vector \(\mathbf{v}\) from \( P_1 \) to \( P_2 \), then finding the length of \(\mathbf{v}\). Use the square root symbol '\(\sqrt{}\)' where needed to give an exact value for your answer.
**Vector Calculation:**
\[
\mathbf{v} =
\begin{bmatrix}
0 \\
0 \\
0 \\
\end{bmatrix}
\]
**Distance Calculation:**
\[
d = 0
\]
**Explanation:**
- The vector \(\mathbf{v}\) and the distance \(d\) should be calculated accurately based on the coordinates of the points \( P_1 \) and \( P_2 \).
- Typically, the elements of the vector \(\mathbf{v}\) are obtained by subtracting the coordinates of \( P_1 \) from those of \( P_2 \).
- The length \(d\) is the magnitude of the vector \(\mathbf{v}\), calculated using the Euclidean formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}
\]
Ensure the correct calculations are followed for accuracy in educational materials.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd4f4b624-9180-41b5-94fa-c093ec7455d7%2F7eae3f82-8b13-40a1-8691-fdfa8e0400ca%2Fmx20n9_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Description:**
Find the distance \( d \) between the points \( P_1(7, 1, 10) \) and \( P_2(-3, 10, 3) \) by first finding the vector \(\mathbf{v}\) from \( P_1 \) to \( P_2 \), then finding the length of \(\mathbf{v}\). Use the square root symbol '\(\sqrt{}\)' where needed to give an exact value for your answer.
**Vector Calculation:**
\[
\mathbf{v} =
\begin{bmatrix}
0 \\
0 \\
0 \\
\end{bmatrix}
\]
**Distance Calculation:**
\[
d = 0
\]
**Explanation:**
- The vector \(\mathbf{v}\) and the distance \(d\) should be calculated accurately based on the coordinates of the points \( P_1 \) and \( P_2 \).
- Typically, the elements of the vector \(\mathbf{v}\) are obtained by subtracting the coordinates of \( P_1 \) from those of \( P_2 \).
- The length \(d\) is the magnitude of the vector \(\mathbf{v}\), calculated using the Euclidean formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}
\]
Ensure the correct calculations are followed for accuracy in educational materials.
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