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D. Complete the parallelogram below. Determine the length of the each side. Show that Proja + Proj-a = a. f TITIT a 10 20 30 40 50 60 70 80 90 J a

D. Complete the parallelogram below. Determine the length of the each side. Show that Proja + Proj-a = a. f TITIT a 10 20 30 40 50 60 70 80 90 J a

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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Complete the parallelogram below. Determine the length of the each side. Show that ProjNa + ProjTa = a.

**Transcription for Educational Website** **Title:** Vector Projections and Parallelogram Completion **Content:** **D. Exercise: Complete the parallelogram below. Determine the length of each side. Show that \( \text{Proj}_{\mathbf{N}} \mathbf{a} + \text{Proj}_{\mathbf{T}} \mathbf{a} = \mathbf{a} \).** **Diagram Explanation:** The given diagram illustrates a vector analysis involving projections. Key elements of the diagram include: - **Vectors:** - \( \mathbf{T} \) and \( \mathbf{N} \) are shown as red arrows representing two different vectors. - \( \mathbf{a} \) is a green arrow representing another vector. - **Axes:** - The graph includes labeled axes with degrees marked from 10 to 90, allowing for angular reference. - **Curves and Components:** - A blue curve is displayed, likely representing a path or a function graph. - Dotted red and black lines indicate potential components or pathways of the vector projection. **Objective:** The task is to complete the parallelogram formed by these vectors and verify that the sum of the projections of vector \( \mathbf{a} \) onto vectors \( \mathbf{N} \) and \( \mathbf{T} \) equals the vector \( \mathbf{a} \) itself. This involves calculating the magnitudes using projection formulas and demonstrating the vector addition graphically within the diagram.
Transcribed Image Text:**Transcription for Educational Website** **Title:** Vector Projections and Parallelogram Completion **Content:** **D. Exercise: Complete the parallelogram below. Determine the length of each side. Show that \( \text{Proj}_{\mathbf{N}} \mathbf{a} + \text{Proj}_{\mathbf{T}} \mathbf{a} = \mathbf{a} \).** **Diagram Explanation:** The given diagram illustrates a vector analysis involving projections. Key elements of the diagram include: - **Vectors:** - \( \mathbf{T} \) and \( \mathbf{N} \) are shown as red arrows representing two different vectors. - \( \mathbf{a} \) is a green arrow representing another vector. - **Axes:** - The graph includes labeled axes with degrees marked from 10 to 90, allowing for angular reference. - **Curves and Components:** - A blue curve is displayed, likely representing a path or a function graph. - Dotted red and black lines indicate potential components or pathways of the vector projection. **Objective:** The task is to complete the parallelogram formed by these vectors and verify that the sum of the projections of vector \( \mathbf{a} \) onto vectors \( \mathbf{N} \) and \( \mathbf{T} \) equals the vector \( \mathbf{a} \) itself. This involves calculating the magnitudes using projection formulas and demonstrating the vector addition graphically within the diagram.
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