Two vectors are being added, one at an angle of 20.0 , and the other at80.0 . The only thing you know about the magnitudes is they are both positive. Will the equilibrant vector be in the (a) first quadrant, (b) second quadrant, (c) third quadrant, (d) fourth quadrant or (e) you cannot tell which quadrant from the available information?

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
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Chapter1: Functions And Models
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**Title: Understanding Vector Addition and Equilibrant Vector Quadrants**

**Article Body:**

In the study of vectors and their applications in various fields such as physics and engineering, understanding how to determine the resultant and equilibrant vectors of multiple vectors is essential. In this lesson, we will explore a problem involving the addition of two vectors, focusing on determining the quadrant in which the equilibrant vector lies.

**Problem Statement:**

Two vectors are being added, one at an angle of 20.0°, and the other at 80.0°. The only information given is that both magnitudes are positive. Which of the following quadrants will the equilibrant vector be in?
- (a) First Quadrant
- (b) Second Quadrant
- (c) Third Quadrant
- (d) Fourth Quadrant
- (e) Cannot tell which quadrant from the available information

**Explanation:**

When adding two vectors, the equilibrant vector is defined as the vector that has the same magnitude as the resultant vector but points in the opposite direction. To determine the quadrant in which the equilibrant vector lies, let's consider the vectors given:

1. **Vector A**: With an angle of 20.0°
2. **Vector B**: With an angle of 80.0°

Both angles are measured counterclockwise from the positive x-axis. 

Since both magnitudes are positive and the angles are within the first quadrant (0° to 90°), both vectors lie in the first quadrant. When two vectors in the first quadrant are added, their resultant vector will also lie in the first quadrant.

The direction of the equilibrant vector will be opposite to that of the resultant vector. Therefore, if the resultant vector lies in the first quadrant, the equilibrant vector will point in the opposite direction and thus lie in the third quadrant.

**Conclusion:**

Based on the information provided, the equilibrant vector will be in the:

- (c) Third quadrant.

Understanding vector addition and equilibrant vectors is crucial for solving various problems related to forces, motions, and other vector-related scenarios. Having a clear conceptual grasp of these principles aids in the accurate analysis and practical application of vectors in real-world situations.
Transcribed Image Text:**Title: Understanding Vector Addition and Equilibrant Vector Quadrants** **Article Body:** In the study of vectors and their applications in various fields such as physics and engineering, understanding how to determine the resultant and equilibrant vectors of multiple vectors is essential. In this lesson, we will explore a problem involving the addition of two vectors, focusing on determining the quadrant in which the equilibrant vector lies. **Problem Statement:** Two vectors are being added, one at an angle of 20.0°, and the other at 80.0°. The only information given is that both magnitudes are positive. Which of the following quadrants will the equilibrant vector be in? - (a) First Quadrant - (b) Second Quadrant - (c) Third Quadrant - (d) Fourth Quadrant - (e) Cannot tell which quadrant from the available information **Explanation:** When adding two vectors, the equilibrant vector is defined as the vector that has the same magnitude as the resultant vector but points in the opposite direction. To determine the quadrant in which the equilibrant vector lies, let's consider the vectors given: 1. **Vector A**: With an angle of 20.0° 2. **Vector B**: With an angle of 80.0° Both angles are measured counterclockwise from the positive x-axis. Since both magnitudes are positive and the angles are within the first quadrant (0° to 90°), both vectors lie in the first quadrant. When two vectors in the first quadrant are added, their resultant vector will also lie in the first quadrant. The direction of the equilibrant vector will be opposite to that of the resultant vector. Therefore, if the resultant vector lies in the first quadrant, the equilibrant vector will point in the opposite direction and thus lie in the third quadrant. **Conclusion:** Based on the information provided, the equilibrant vector will be in the: - (c) Third quadrant. Understanding vector addition and equilibrant vectors is crucial for solving various problems related to forces, motions, and other vector-related scenarios. Having a clear conceptual grasp of these principles aids in the accurate analysis and practical application of vectors in real-world situations.
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