What is the unit-vector notation for each of the following vectors, all with magnitudes of 50.0? (a) Vector é with direction of 70.0° counterclockwise from the +x-axis. E = (b) Vector F with direction of 70.0° counterclockwise from the +y-axis. F = (c) Vector G with direction of 70.0° clockwise from the -y-axis.
What is the unit-vector notation for each of the following vectors, all with magnitudes of 50.0? (a) Vector é with direction of 70.0° counterclockwise from the +x-axis. E = (b) Vector F with direction of 70.0° counterclockwise from the +y-axis. F = (c) Vector G with direction of 70.0° clockwise from the -y-axis.
College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![**Unit-Vector Notation for Vectors with Specific Directions and Magnitudes**
The following vectors are defined by their directions and magnitudes. The task is to express each vector in unit-vector notation. A unit vector specifies direction and has a magnitude of one. Points are designated counterclockwise from specific axes unless noted otherwise. All vectors have magnitudes of 50.0 units.
**(a) Vector \( \vec{E} \) with a direction of 70.0° counterclockwise from the +x-axis.**
\[ \vec{E} = \]
**(b) Vector \( \vec{F} \) with a direction of 70.0° counterclockwise from the +y-axis.**
\[ \vec{F} = \]
**(c) Vector \( \vec{G} \) with a direction of 70.0° clockwise from the -y-axis.**
\[ \vec{G} = \]
### Explanation for Vectors in Unit-Vector Notation
To convert a vector from magnitude and direction to unit-vector notation, use the following steps:
1. **Resolve the Vector into its Components**:
- For a vector with magnitude \( M \) and direction \( \theta \):
\[ \text{Component in x-direction} = M \cos(\theta) \]
\[ \text{Component in y-direction} = M \sin(\theta) \]
2. **Express in î and ĵ Notation**:
- Represent the x-component with î and the y-component with ĵ.
**For Vector \( \vec{E} \):**
- Magnitude = 50.0
- Direction = 70.0° counterclockwise from the +x-axis.
\[ \vec{E} = 50.0 \cos(70.0°) \, \hat{i} + 50.0 \sin(70.0°) \, \hat{j} \]
**For Vector \( \vec{F} \):**
- Magnitude = 50.0
- Direction = 70.0° counterclockwise from the +y-axis.
- Note: The angle from the +y-axis needs to be adjusted for standard positioning (i.e., from the +x-axis).
\[ \vec{F} = 50.0 \cos(160.0°) \, \hat{i} +](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa023f3c3-3186-4c61-aa74-30f5825e9d0f%2Fef521973-8f33-463b-98e1-b62deff3f7cf%2F2hfohaj.jpeg&w=3840&q=75)
Transcribed Image Text:**Unit-Vector Notation for Vectors with Specific Directions and Magnitudes**
The following vectors are defined by their directions and magnitudes. The task is to express each vector in unit-vector notation. A unit vector specifies direction and has a magnitude of one. Points are designated counterclockwise from specific axes unless noted otherwise. All vectors have magnitudes of 50.0 units.
**(a) Vector \( \vec{E} \) with a direction of 70.0° counterclockwise from the +x-axis.**
\[ \vec{E} = \]
**(b) Vector \( \vec{F} \) with a direction of 70.0° counterclockwise from the +y-axis.**
\[ \vec{F} = \]
**(c) Vector \( \vec{G} \) with a direction of 70.0° clockwise from the -y-axis.**
\[ \vec{G} = \]
### Explanation for Vectors in Unit-Vector Notation
To convert a vector from magnitude and direction to unit-vector notation, use the following steps:
1. **Resolve the Vector into its Components**:
- For a vector with magnitude \( M \) and direction \( \theta \):
\[ \text{Component in x-direction} = M \cos(\theta) \]
\[ \text{Component in y-direction} = M \sin(\theta) \]
2. **Express in î and ĵ Notation**:
- Represent the x-component with î and the y-component with ĵ.
**For Vector \( \vec{E} \):**
- Magnitude = 50.0
- Direction = 70.0° counterclockwise from the +x-axis.
\[ \vec{E} = 50.0 \cos(70.0°) \, \hat{i} + 50.0 \sin(70.0°) \, \hat{j} \]
**For Vector \( \vec{F} \):**
- Magnitude = 50.0
- Direction = 70.0° counterclockwise from the +y-axis.
- Note: The angle from the +y-axis needs to be adjusted for standard positioning (i.e., from the +x-axis).
\[ \vec{F} = 50.0 \cos(160.0°) \, \hat{i} +
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