Question
\[ \vec{v}+\vec{v}=\langle 0.21,14.03\rangle \] c. In what quadrant does the resultant vector lie?
Ask by Goodwin Hodgson. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The resultant vector lies in the first quadrant.
Solution
The resultant vector is given by \(\langle 0.21, 14.03 \rangle\).
To determine the quadrant in which this vector lies, we examine the signs of its components:
- **x-component**: \(0.21\) (positive)
- **y-component**: \(14.03\) (positive)
Since both the x and y components are positive, the vector lies in **Quadrant I**.
**Answer:** The resultant vector lies in the first quadrant.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
First off, let's break down the given vector equation! You've got \(\vec{v} + \vec{v} = \langle 0.21, 14.03 \rangle\). Simplifying this, you can see that \(2\vec{v} = \langle 0.21, 14.03 \rangle\), which means \(\vec{v} = \langle 0.105, 7.015 \rangle\). Now, regarding the quadrant: The "x" component (0.105) is positive and the "y" component (7.015) is also positive. This places the resultant vector squarely in the first quadrant, where both x and y values are greater than zero. So, joyfully wave hello to Quadrant I! If you’re ever unsure about quadrant placement, just remember: Quadrant I is where the magic happens—with both positive x and positive y driving the party!
