College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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![The **dot product** is one way of multiplying two vectors.
---
### Part A
*(Figure 1) shows two vectors* **\(\vec{A}\)** *and* **\(\vec{B}\)**. *What is their dot product?*
- **Figure Description**:
- Two vectors are shown, labeled \(\vec{A}\) and \(\vec{B}\).
- The angle between the two vectors is \(60^\circ\).
- The magnitude of vector \(\vec{A}\) is 3.
- The magnitude of vector \(\vec{B}\) is 4.
- **Dot Product Calculation**:
- \(\vec{A} \cdot \vec{B} =\) [Enter the dot product here]
- **Submit Button**
---
### Part B
*Vector* **\(\vec{C} = 2\hat{i} + 4\hat{j}\)**, *and vector* **\(\vec{D} = 3\hat{i} - \hat{j}\)**. *What is their dot product?*
- **Dot Product Calculation**:
- \(\vec{C} \cdot \vec{D} =\) [Enter the dot product here]
- **Submit Button**](https://content.bartleby.com/qna-images/question/e6ce2240-b3fe-4331-98ee-3937416f40f5/b64b2250-b342-487c-a4ec-8afdbf5cdcb5/lhzovnc_processed.png)
Transcribed Image Text:The **dot product** is one way of multiplying two vectors.
---
### Part A
*(Figure 1) shows two vectors* **\(\vec{A}\)** *and* **\(\vec{B}\)**. *What is their dot product?*
- **Figure Description**:
- Two vectors are shown, labeled \(\vec{A}\) and \(\vec{B}\).
- The angle between the two vectors is \(60^\circ\).
- The magnitude of vector \(\vec{A}\) is 3.
- The magnitude of vector \(\vec{B}\) is 4.
- **Dot Product Calculation**:
- \(\vec{A} \cdot \vec{B} =\) [Enter the dot product here]
- **Submit Button**
---
### Part B
*Vector* **\(\vec{C} = 2\hat{i} + 4\hat{j}\)**, *and vector* **\(\vec{D} = 3\hat{i} - \hat{j}\)**. *What is their dot product?*
- **Dot Product Calculation**:
- \(\vec{C} \cdot \vec{D} =\) [Enter the dot product here]
- **Submit Button**
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Transcribed Image Text:**Educational Content Transcription**
**Diagram Explanation:**
The diagram is a Cartesian coordinate system with x and y axes. It features two vectors, labeled \(\vec{E}\) and \(\vec{F}\), originating from the same point on the origin.
- **Vector \(\vec{E}\):** Points in the first quadrant, approximately extending to (3, 3) in the x and y axes.
- **Vector \(\vec{F}\):** Points in the fourth quadrant, approximately extending to (4, -3) in the x and y axes.
The angle \(\theta\) between vectors \(\vec{E}\) and \(\vec{F}\) at their common origin is marked.
**Question Detail:**
- The prompt asks: "What is the angle \(\theta\) between vectors \(\vec{E}\) and \(\vec{F}\)?"
- The answer should be expressed in degrees.
**Submission Section:**
- There is an input box for entering the value of \(\theta\) accompanied by a submit button.
- Users can view available hints by clicking on the "View Available Hint(s)" option.
Solution
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Follow-up Question
Transcribed Image Text:**Educational Content Transcription**
**Diagram Explanation:**
The diagram is a Cartesian coordinate system with x and y axes. It features two vectors, labeled \(\vec{E}\) and \(\vec{F}\), originating from the same point on the origin.
- **Vector \(\vec{E}\):** Points in the first quadrant, approximately extending to (3, 3) in the x and y axes.
- **Vector \(\vec{F}\):** Points in the fourth quadrant, approximately extending to (4, -3) in the x and y axes.
The angle \(\theta\) between vectors \(\vec{E}\) and \(\vec{F}\) at their common origin is marked.
**Question Detail:**
- The prompt asks: "What is the angle \(\theta\) between vectors \(\vec{E}\) and \(\vec{F}\)?"
- The answer should be expressed in degrees.
**Submission Section:**
- There is an input box for entering the value of \(\theta\) accompanied by a submit button.
- Users can view available hints by clicking on the "View Available Hint(s)" option.
Solution
by Bartleby Expert
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- Evaluate the cross product A×B if A = 39, B = 59 and θ = 43°. Evaluate the cross product C×D if C = 23 and D = 83. The angle between them is a right angle.arrow_forwardGiven the pair of vectors, A = (9.00î − 5.00ĵ ) and B =(−3.00î + 9.00ĵ ),use the definition of a scalar product to determine the following. (a) the scalar product (b) the angle between the vectors (Enter an answer between 0 and 180 degrees.) ° (c) the angle ? between the vector A and the +x axis (Enter an answer between 0 and 180 degrees.) ° (d) the angle ? between the vector B and the +y axis (Enter an answer between 0 and 180 degrees.) °arrow_forwardThe scalar product of vectors A and B is +50.0 m². Vector A has magnitude 6.00 m and direction 28.0° west of south. Part A If vector B has direction 39.0° south of east, what is the magnitude of B? Express your answer with the appropriate units. μA B = Value Submit Request Answer Units ?arrow_forward
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