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In Exercises 3-4, find the components 3. a. P₁(3,5), P₂(2,8) of the vector P₁P₂. b. P₁(5, −2,1), P₂(2,4, 2)

In Exercises 3-4, find the components 3. a. P₁(3,5), P₂(2,8) of the vector P₁P₂. b. P₁(5, −2,1), P₂(2,4, 2)

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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**Exercise 3-4: Finding the Components of a Vector** In Exercises 3–4, find the components of the vector \( \overrightarrow{P_1 P_2} \). **Exercise 3:** - **a.** \( P_1(3, 5) \), \( P_2(2, 8) \) - **b.** \( P_1(5, -2, 1) \), \( P_2(2, 4, 2) \) For each pair of points \( P_1 \) and \( P_2 \), you will need to calculate the vector \( \overrightarrow{P_1 P_2} = P_2 - P_1 \) by subtracting the coordinates of \( P_1 \) from \( P_2 \). - For part a, the points are in two-dimensional space: - \( \vec{P_1P_2} = (2 - 3, 8 - 5) \) - For part b, the points are in three-dimensional space: - \( \vec{P_1P_2} = (2 - 5, 4 - (-2), 2 - 1) \) Work through the subtractions to find the components of the vectors for each part.
Transcribed Image Text:**Exercise 3-4: Finding the Components of a Vector** In Exercises 3–4, find the components of the vector \( \overrightarrow{P_1 P_2} \). **Exercise 3:** - **a.** \( P_1(3, 5) \), \( P_2(2, 8) \) - **b.** \( P_1(5, -2, 1) \), \( P_2(2, 4, 2) \) For each pair of points \( P_1 \) and \( P_2 \), you will need to calculate the vector \( \overrightarrow{P_1 P_2} = P_2 - P_1 \) by subtracting the coordinates of \( P_1 \) from \( P_2 \). - For part a, the points are in two-dimensional space: - \( \vec{P_1P_2} = (2 - 3, 8 - 5) \) - For part b, the points are in three-dimensional space: - \( \vec{P_1P_2} = (2 - 5, 4 - (-2), 2 - 1) \) Work through the subtractions to find the components of the vectors for each part.
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