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![**HW 02: 1D Kinematics and Vectors**
**Item 17**
---
### Part C
**Question:**
What is the angle between vectors **E** \( = 5\hat{i} + 7\hat{k} \) and **F** \( = 8\hat{j} - 1\hat{k} \)?
**Instruction:**
Express your answer as an angle in degrees between 0° and 180°.
**Answer Input Section:**
Include a text box for students to enter their answer.
**Buttons Available:**
- Submit
- Request Answer
---
### Part D
**Question:**
What is the angle between vectors **G** \( = 1\hat{i} + 10\hat{j} + 2\hat{k} \) and **H** \( = 2\hat{i} + 1\hat{j} + 1\hat{k} \)?
**Instruction:**
Express your answer as an angle in degrees between 0° and 180°.
**Answer Input Section:**
Include a text box for students to enter their answer.
**Buttons Available:**
- Submit
- Request Answer
---
**Navigation Options:**
- Return to Assignment
- Provide Feedback
(Note: The image does not contain any graphs or diagrams that require detailed explanations.)
---
### Explanation for Educational Purposes:
To find the angle between two vectors, you can use the dot product formula:
\[ \textbf{A} \cdot \textbf{B} = | \textbf{A} | | \textbf{B} | \cos \theta \]
Where:
- \(\textbf{A} \cdot \textbf{B}\) is the dot product of vectors \(\textbf{A}\) and \(\textbf{B}\).
- \(| \textbf{A} |\) and \(| \textbf{B} |\) are the magnitudes (lengths) of vectors \(\textbf{A}\) and \(\textbf{B}\).
- \(\theta\) is the angle between the two vectors.
**Steps:**
1. Calculate the dot product of the two vectors.
2. Calculate the magnitudes of each vector.
3. Rearrange the dot product formula to solve for \(\cos \theta\).
4. Use the inverse cosine (arcc](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a5bf8ad-4965-4e63-b21c-5c2ad3e92a8d%2Fd9335e0a-6249-49d9-a8a3-df5512407d3f%2Fc7xhm6c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**HW 02: 1D Kinematics and Vectors**
**Item 17**
---
### Part C
**Question:**
What is the angle between vectors **E** \( = 5\hat{i} + 7\hat{k} \) and **F** \( = 8\hat{j} - 1\hat{k} \)?
**Instruction:**
Express your answer as an angle in degrees between 0° and 180°.
**Answer Input Section:**
Include a text box for students to enter their answer.
**Buttons Available:**
- Submit
- Request Answer
---
### Part D
**Question:**
What is the angle between vectors **G** \( = 1\hat{i} + 10\hat{j} + 2\hat{k} \) and **H** \( = 2\hat{i} + 1\hat{j} + 1\hat{k} \)?
**Instruction:**
Express your answer as an angle in degrees between 0° and 180°.
**Answer Input Section:**
Include a text box for students to enter their answer.
**Buttons Available:**
- Submit
- Request Answer
---
**Navigation Options:**
- Return to Assignment
- Provide Feedback
(Note: The image does not contain any graphs or diagrams that require detailed explanations.)
---
### Explanation for Educational Purposes:
To find the angle between two vectors, you can use the dot product formula:
\[ \textbf{A} \cdot \textbf{B} = | \textbf{A} | | \textbf{B} | \cos \theta \]
Where:
- \(\textbf{A} \cdot \textbf{B}\) is the dot product of vectors \(\textbf{A}\) and \(\textbf{B}\).
- \(| \textbf{A} |\) and \(| \textbf{B} |\) are the magnitudes (lengths) of vectors \(\textbf{A}\) and \(\textbf{B}\).
- \(\theta\) is the angle between the two vectors.
**Steps:**
1. Calculate the dot product of the two vectors.
2. Calculate the magnitudes of each vector.
3. Rearrange the dot product formula to solve for \(\cos \theta\).
4. Use the inverse cosine (arcc
![### HW 02: 1D Kinematics and Vectors
#### Item 17
**Part A**
What is the angle between vectors \(\vec{A} = -2\hat{i} + 7\hat{j}\) and \(\vec{B} = -6\hat{i} + -2\hat{j}\)?
*Express your answer as an angle in degrees between 0° and 180°.*
\[ \vec{A} = -2\hat{i} + 7\hat{j} \]
\[ \vec{B} = -6\hat{i} + -2\hat{j} \]
<div>
<input type="text" placeholder="Enter your answer here">
<button>Submit</button>
<button>Request Answer</button>
</div>
**Part B**
What is the angle between vectors \(\vec{C} = 5\hat{i} + 3\hat{j}\) and \(\vec{D} = 6\hat{i} - 10\hat{j}\)?
*Express your answer as an angle in degrees between 0° and 180°.*
\[ \vec{C} = 5\hat{i} + 3\hat{j} \]
\[ \vec{D} = 6\hat{i} - 10\hat{j} \]
<div>
<input type="text" placeholder="Enter your answer here">
<button>Submit</button>
<button>Request Answer</button>
</div>
**Part C**
This part might involve additional problems or theoretical questions as follow-ups to Part A and Part B. Please solve the first two parts to proceed to Part C.
<div>
<input type="text" placeholder="Solve earlier parts to unlock">
</div>
---
For educational purposes, follow these steps to calculate the angle between two vectors:
1. **Dot Product of Vectors:** \(\vec{A} \cdot \vec{B} = A_x B_x + A_y B_y\)
2. **Magnitude of Vectors:**
- \(|\vec{A}| = \sqrt{A_x^2 + A_y^2}\)
- \(|\vec{B}| = \sqrt{B_x^2 + B_y^2}\)
3. **Angle Calculation:**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a5bf8ad-4965-4e63-b21c-5c2ad3e92a8d%2Fd9335e0a-6249-49d9-a8a3-df5512407d3f%2Fbhx4lhc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### HW 02: 1D Kinematics and Vectors
#### Item 17
**Part A**
What is the angle between vectors \(\vec{A} = -2\hat{i} + 7\hat{j}\) and \(\vec{B} = -6\hat{i} + -2\hat{j}\)?
*Express your answer as an angle in degrees between 0° and 180°.*
\[ \vec{A} = -2\hat{i} + 7\hat{j} \]
\[ \vec{B} = -6\hat{i} + -2\hat{j} \]
<div>
<input type="text" placeholder="Enter your answer here">
<button>Submit</button>
<button>Request Answer</button>
</div>
**Part B**
What is the angle between vectors \(\vec{C} = 5\hat{i} + 3\hat{j}\) and \(\vec{D} = 6\hat{i} - 10\hat{j}\)?
*Express your answer as an angle in degrees between 0° and 180°.*
\[ \vec{C} = 5\hat{i} + 3\hat{j} \]
\[ \vec{D} = 6\hat{i} - 10\hat{j} \]
<div>
<input type="text" placeholder="Enter your answer here">
<button>Submit</button>
<button>Request Answer</button>
</div>
**Part C**
This part might involve additional problems or theoretical questions as follow-ups to Part A and Part B. Please solve the first two parts to proceed to Part C.
<div>
<input type="text" placeholder="Solve earlier parts to unlock">
</div>
---
For educational purposes, follow these steps to calculate the angle between two vectors:
1. **Dot Product of Vectors:** \(\vec{A} \cdot \vec{B} = A_x B_x + A_y B_y\)
2. **Magnitude of Vectors:**
- \(|\vec{A}| = \sqrt{A_x^2 + A_y^2}\)
- \(|\vec{B}| = \sqrt{B_x^2 + B_y^2}\)
3. **Angle Calculation:**
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