### Unit-Vector Notation for Given VectorsGiven the vectors below, all with magnitudes of 41.5, determine their unit-vector notations.(a) **Vector \(\vec{E}\)** with a direction of 75.0° counterclockwise from the +x-axis.\[\vec{E} = \](b) **Vector \(\vec{F}\)** with a direction of 75.0° counterclockwise from the +y-axis.\[\vec{F} = \](c) **Vector \(\vec{G}\)** with a direction of 75.0° clockwise from the −y-axis.\[\vec{G} = \]#### Explanation:1. **For Vector \(\vec{E}\)**: To find the unit vector notation, decompose it into its x and y components using the given angle and magnitude. 2. **For Vector \(\vec{F}\)**: Similarly, decompose this vector into components, noting the direction relative to the +y-axis.3. **For Vector \(\vec{G}\)**: Again, decompose this vector into components, noting that the angle is measured clockwise from the −y-axis.If you need additional help with the concepts or solving the problems, click on "Read It" for further assistance.

Part(a): Direction of is counter-clockwise from +x-axis and its magnitude is Part(b): Direction of…

Answered: What is the unit-vector notation for…

What is the unit-vector notation for each of the following vectors, all with magnitudes of 41.5? (a) Vector E with direction of 75.0° counterclockwise from the +x-axis.

College Physics

11th Edition

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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Scalars and Vectors

Scalars and Vectors are the classification of physical quantities that are used to denote various terms in physics.

Question

### Unit-Vector Notation for Given Vectors

Given the vectors below, all with magnitudes of 41.5, determine their unit-vector notations.

(a) **Vector \(\vec{E}\)** with a direction of 75.0° counterclockwise from the +x-axis.
\[
\vec{E} =
\]

(b) **Vector \(\vec{F}\)** with a direction of 75.0° counterclockwise from the +y-axis.
\[
\vec{F} =
\]

(c) **Vector \(\vec{G}\)** with a direction of 75.0° clockwise from the −y-axis.
\[
\vec{G} =
\]

#### Explanation:
1. **For Vector \(\vec{E}\)**: To find the unit vector notation, decompose it into its x and y components using the given angle and magnitude.

2. **For Vector \(\vec{F}\)**: Similarly, decompose this vector into components, noting the direction relative to the +y-axis.

3. **For Vector \(\vec{G}\)**: Again, decompose this vector into components, noting that the angle is measured clockwise from the −y-axis.

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