2. 4 7 X•w Compute w • w, x•w, and using the vectors w=-1 and x = w•w - 5 3 w•w = (Simplify your answer. Type an integer or a simplified fraction.) x•w = (Simplify your answer. Type an integer or a simplified fraction.) w•w (Simplify your answer. Type an integer or a simplified fraction.) 3.
2. 4 7 X•w Compute w • w, x•w, and using the vectors w=-1 and x = w•w - 5 3 w•w = (Simplify your answer. Type an integer or a simplified fraction.) x•w = (Simplify your answer. Type an integer or a simplified fraction.) w•w (Simplify your answer. Type an integer or a simplified fraction.) 3.
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 Operations Exercise
**Problem 2:**
Compute \(\mathbf{w} \cdot \mathbf{w}\), \(\mathbf{x} \cdot \mathbf{w}\), and \(\frac{\mathbf{x} \cdot \mathbf{w}}{\mathbf{w} \cdot \mathbf{w}}\) using the vectors \(\mathbf{w}\) and \(\mathbf{x}\).
Given vectors:
\[
\mathbf{w} =
\begin{bmatrix}
4 \\
-1 \\
-5
\end{bmatrix},
\quad \text{and} \quad
\mathbf{x} =
\begin{bmatrix}
7 \\
-3 \\
3
\end{bmatrix}
\]
### Tasks:
1. Calculate \(\mathbf{w} \cdot \mathbf{w}\)
\[
\mathbf{w} \cdot \mathbf{w} = \underline{\hspace{2cm}}
\]
*(Simplify your answer. Type an integer or a simplified fraction.)*
2. Calculate \(\mathbf{x} \cdot \mathbf{w}\)
\[
\mathbf{x} \cdot \mathbf{w} = \underline{\hspace{2cm}}
\]
*(Simplify your answer. Type an integer or a simplified fraction.)*
3. Calculate \(\frac{\mathbf{x} \cdot \mathbf{w}}{\mathbf{w} \cdot \mathbf{w}}\)
\[
\frac{\mathbf{x} \cdot \mathbf{w}}{\mathbf{w} \cdot \mathbf{w}} = \underline{\hspace{2cm}}
\]
*(Simplify your answer. Type an integer or a simplified fraction.)*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F47d7a0f8-4e66-40ed-ae66-faa7d8f664d3%2F3c48a832-5bb8-4fe2-a1f4-6f85c0b13e7c%2F9bx8kd4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Vector Operations Exercise
**Problem 2:**
Compute \(\mathbf{w} \cdot \mathbf{w}\), \(\mathbf{x} \cdot \mathbf{w}\), and \(\frac{\mathbf{x} \cdot \mathbf{w}}{\mathbf{w} \cdot \mathbf{w}}\) using the vectors \(\mathbf{w}\) and \(\mathbf{x}\).
Given vectors:
\[
\mathbf{w} =
\begin{bmatrix}
4 \\
-1 \\
-5
\end{bmatrix},
\quad \text{and} \quad
\mathbf{x} =
\begin{bmatrix}
7 \\
-3 \\
3
\end{bmatrix}
\]
### Tasks:
1. Calculate \(\mathbf{w} \cdot \mathbf{w}\)
\[
\mathbf{w} \cdot \mathbf{w} = \underline{\hspace{2cm}}
\]
*(Simplify your answer. Type an integer or a simplified fraction.)*
2. Calculate \(\mathbf{x} \cdot \mathbf{w}\)
\[
\mathbf{x} \cdot \mathbf{w} = \underline{\hspace{2cm}}
\]
*(Simplify your answer. Type an integer or a simplified fraction.)*
3. Calculate \(\frac{\mathbf{x} \cdot \mathbf{w}}{\mathbf{w} \cdot \mathbf{w}}\)
\[
\frac{\mathbf{x} \cdot \mathbf{w}}{\mathbf{w} \cdot \mathbf{w}} = \underline{\hspace{2cm}}
\]
*(Simplify your answer. Type an integer or a simplified fraction.)*
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