Vector component of V and W are as follows. Find the direction of the resultant vector. V= (13.5, -21.07) W = (-0.9, -14.6) [?]° Round to the nearest hundredth. Enter
Vector component of V and W are as follows. Find the direction of the resultant vector. V= (13.5, -21.07) W = (-0.9, -14.6) [?]° Round to the nearest hundredth. Enter
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
![**Vectors and Directions: An Educational Exploration**
**Problem Statement:**
You are given the vector components of \(\vec{v}\) and \(\vec{w}\) as follows. Your task is to find the direction of the resultant vector.
**Components:**
- \(\vec{v} = (13.5, -21.07)\)
- \(\vec{w} = (-0.9, -14.6)\)
**Problem:**
Calculate the direction of the resultant vector \(\vec{r} = \vec{v} + \vec{w}\).
**Solution Steps:**
1. **Add the Vectors:**
\[
\vec{r} = \vec{v} + \vec{w} = (13.5 - 0.9, -21.07 - 14.6)
\]
\[
\vec{r} = (12.6, -35.67)
\]
2. **Find the Direction:**
- The direction \(\theta\) (in degrees) of a vector \((x, y)\) is given by:
\[
\theta = \tan^{-1}\left(\frac{y}{x}\right)
\]
3. **Calculate the Angle:**
- Plug in the values:
\[
\theta = \tan^{-1}\left(\frac{-35.67}{12.6}\right)
\]
4. **Round to the Nearest Hundredth:**
- Use a calculator to find the angle and round it as required.
**Answer Box:**
Enter the calculated angle \([\theta]°\) rounded to the nearest hundredth.
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This problem helps to understand the addition of vectors and calculating their resultant direction in a two-dimensional plane.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff2e48c84-501d-43ab-acf7-5d78dee44313%2F13932eb4-b615-4928-82d3-a3667b197fa8%2F1zvx4k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Vectors and Directions: An Educational Exploration**
**Problem Statement:**
You are given the vector components of \(\vec{v}\) and \(\vec{w}\) as follows. Your task is to find the direction of the resultant vector.
**Components:**
- \(\vec{v} = (13.5, -21.07)\)
- \(\vec{w} = (-0.9, -14.6)\)
**Problem:**
Calculate the direction of the resultant vector \(\vec{r} = \vec{v} + \vec{w}\).
**Solution Steps:**
1. **Add the Vectors:**
\[
\vec{r} = \vec{v} + \vec{w} = (13.5 - 0.9, -21.07 - 14.6)
\]
\[
\vec{r} = (12.6, -35.67)
\]
2. **Find the Direction:**
- The direction \(\theta\) (in degrees) of a vector \((x, y)\) is given by:
\[
\theta = \tan^{-1}\left(\frac{y}{x}\right)
\]
3. **Calculate the Angle:**
- Plug in the values:
\[
\theta = \tan^{-1}\left(\frac{-35.67}{12.6}\right)
\]
4. **Round to the Nearest Hundredth:**
- Use a calculator to find the angle and round it as required.
**Answer Box:**
Enter the calculated angle \([\theta]°\) rounded to the nearest hundredth.
<footer>National Academy of Science. All Rights Reserved.</footer>
This problem helps to understand the addition of vectors and calculating their resultant direction in a two-dimensional plane.
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