https://file.aiquickdraw.com/mathbot/file/1726009773230qgvxom0g.jpg

Let's analyze the vectors described in the image to solve for the largest x-component and y-component.

1. **Vector A**: It points along the **+y-axis** and has a magnitude of **100 units**. Since it's along the y-axis, its x-component is 0, and its y-component is 100.

2. **Vector B**: It points at an angle of **60° above the +x-axis** and has a magnitude of **200 units**. We can resolve this vector into its components:
   - \( x_B = 200 \cdot \cos(60^\circ) = 200 \cdot 0.5 = 100 \)
   - \( y_B = 200 \cdot \sin(60^\circ) = 200 \cdot \frac{\sqrt{3}}{2} \approx 200 \cdot 0.866 = 173.2 \)

3. **Vector C**: It points along the **+x-axis** and has a magnitude of **150 units**. Since it points entirely along the x-axis, its x-component is 150, and its y-component is 0.

Now, let's determine which vector has the largest x-component and y-component:

- **x-components**:
   - Vector A: 0
   - Vector B: 100
   - Vector C: 150

   So, **Vector C** has the largest x-component of 150.

- **y-components**:
   - Vector A: 100
   - Vector B: 173.2
   - Vector C: 0

   So, **Vector B** has the largest y-component of 173.2.

### Answers:
(a) **Vector C** has the largest x-component.  
(b) **Vector B** has the largest y-component.

Would you like further clarification or additional details?

---

Here are 5 related questions to further your understanding:
1. How do you find the angle between two vectors if their components are known?
2. What happens if Vector B had an angle of 45° instead of 60°?
3. Can you explain how to find the resultant vector when two vectors are added together?
4. What is the significance of the dot product of two vectors in 2D space?
5. How would the x and y components change if Vector C were rotated by 30°?

**Tip:** When resolving vectors into components, always consider the angle relative to the axis, and use trigonometric functions accordingly!

Vector A points along the +y-axis and has a magnitude of 100 units. Vector B points at an angle of 60° above the +x-axis and has a magnitude of 200 units. Vector C points along the +x-axis and has a magnitude of 150 units. Which vector has the largest x-component and largest y-component?

Learn how to determine the largest x and y components in a vector problem. This problem involves resolving vector B at an angle of 60° and comparing it with vectors along the x and y axes, utilizing trigonometric functions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation