The initial point of a vector v in V₂ is the origin and the terminal point is in quadrant II. If v makes an angle with the positive x-axis and |v| = 6, find v in component form 6
The initial point of a vector v in V₂ is the origin and the terminal point is in quadrant II. If v makes an angle with the positive x-axis and |v| = 6, find v in component form 6
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 39RE
Related questions
Question
100%
![### Vector Component Calculation
The initial point of a vector **v** in \( \mathbb{V}_2 \) is the origin, and the terminal point is in quadrant II. If vector **v** makes an angle of \( \frac{5\pi}{6} \) with the positive x-axis and \( |v| = 6 \), find **v** in component form.
**\[ \mathbf{v} = \big[ \text{Input Box} \big] \]**
**Explanation:**
1. The given angle \( \frac{5\pi}{6} \) is in radians.
2. The magnitude of the vector |**v**| is 6.
3. The vector **v** is situated in Quadrant II, hence the x-component will be negative while the y-component will be positive.
We can calculate the components of vector **v** using the formulas:
- \( v_x = |v| \cos\theta \)
- \( v_y = |v| \sin\theta \)
Where \( \theta = \frac{5\pi}{6} \).
\[
v_x = 6 \cos\left(\frac{5\pi}{6}\right)
\]
\[
v_y = 6 \sin\left(\frac{5\pi}{6}\right)
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab6b79a9-c663-4f87-993a-883a678be91b%2F83aa5cd9-11fa-40ed-8463-c845387602e7%2F1rokcc_processed.png&w=3840&q=75)
Transcribed Image Text:### Vector Component Calculation
The initial point of a vector **v** in \( \mathbb{V}_2 \) is the origin, and the terminal point is in quadrant II. If vector **v** makes an angle of \( \frac{5\pi}{6} \) with the positive x-axis and \( |v| = 6 \), find **v** in component form.
**\[ \mathbf{v} = \big[ \text{Input Box} \big] \]**
**Explanation:**
1. The given angle \( \frac{5\pi}{6} \) is in radians.
2. The magnitude of the vector |**v**| is 6.
3. The vector **v** is situated in Quadrant II, hence the x-component will be negative while the y-component will be positive.
We can calculate the components of vector **v** using the formulas:
- \( v_x = |v| \cos\theta \)
- \( v_y = |v| \sin\theta \)
Where \( \theta = \frac{5\pi}{6} \).
\[
v_x = 6 \cos\left(\frac{5\pi}{6}\right)
\]
\[
v_y = 6 \sin\left(\frac{5\pi}{6}\right)
\]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage