Q Write the vector shown below as a combination of vectors and shown above Vector = u u+ V Note: In both graphs, each box is 1 unit by 1 unit in size
Q Write the vector shown below as a combination of vectors and shown above Vector = u u+ V Note: In both graphs, each box is 1 unit by 1 unit in size
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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Question
![**Vector Composition Exercise**
**Graph 1: Vector Representation**
- The graph displays two vectors labeled **\(\vec{u}\)** and **\(\vec{v}\)**.
- **\(\vec{u}\)** is represented as a vector pointing to the right.
- **\(\vec{v}\)** is shown pointing diagonally upwards to the left.
- The grid has standard spacing with each box representing 1 unit by 1 unit.
**Task:**
Write the vector shown in Graph 2 as a combination of vectors **\(\vec{u}\)** and **\(\vec{v}\)** depicted in Graph 1.
**Graph 2: Target Vector**
- This graph illustrates a single vector pointing mostly upwards and slightly to the left.
- The grid is similar, with each box representing 1 unit by 1 unit.
**Equation:**
\[ \text{Vector} = a \cdot \vec{u} + b \cdot \vec{v} \]
**Note:**
- Determine the coefficients \(a\) and \(b\) that express the target vector as a combination of **\(\vec{u}\)** and **\(\vec{v}\)**.
- Use the "Calculator" for assistance in calculating coefficients.
- Confirm your results by selecting "Check Answer."
This exercise involves vector addition, which is fundamental in understanding linear combinations and vector spaces.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa79c18d0-6a0e-4a38-9496-04f82bd62d69%2F6a952f8a-aaa8-4be1-9fe1-60f804600600%2Fycbtuoi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Vector Composition Exercise**
**Graph 1: Vector Representation**
- The graph displays two vectors labeled **\(\vec{u}\)** and **\(\vec{v}\)**.
- **\(\vec{u}\)** is represented as a vector pointing to the right.
- **\(\vec{v}\)** is shown pointing diagonally upwards to the left.
- The grid has standard spacing with each box representing 1 unit by 1 unit.
**Task:**
Write the vector shown in Graph 2 as a combination of vectors **\(\vec{u}\)** and **\(\vec{v}\)** depicted in Graph 1.
**Graph 2: Target Vector**
- This graph illustrates a single vector pointing mostly upwards and slightly to the left.
- The grid is similar, with each box representing 1 unit by 1 unit.
**Equation:**
\[ \text{Vector} = a \cdot \vec{u} + b \cdot \vec{v} \]
**Note:**
- Determine the coefficients \(a\) and \(b\) that express the target vector as a combination of **\(\vec{u}\)** and **\(\vec{v}\)**.
- Use the "Calculator" for assistance in calculating coefficients.
- Confirm your results by selecting "Check Answer."
This exercise involves vector addition, which is fundamental in understanding linear combinations and vector spaces.
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