1. What is Vector Addition and Subtraction?

Vector addition and subtraction are fundamental operations in vector mathematics. When adding two vectors, you add their corresponding components. When subtracting, you subtract the components of the second vector from the first.

2. How Does the Calculator Work?

The calculator performs component-wise operations:

Where:

• \( a_x, a_y \) — Components of vector a
• \( b_x, b_y \) — Components of vector b

Explanation: The calculator simply adds or subtracts the corresponding x and y components of the vectors to produce the result.

3. Importance of Vector Operations

Details: Vector operations are essential in physics, engineering, computer graphics, and many other fields where quantities have both magnitude and direction.

4. Using the Calculator

Tips: Enter the x and y components for both vectors. The calculator will compute and display the sum and difference as ordered pairs (x, y).

5. Frequently Asked Questions (FAQ)

Q1: Can this calculator handle 3D vectors?
A: This version only handles 2D vectors. For 3D vectors, you would need to include a z-component.

Q2: What's the geometric interpretation of vector addition?
A: Vector addition can be visualized using the "tip-to-tail" method, where you place the tail of the second vector at the tip of the first.

Q3: What about vector multiplication?
A: There are different types of vector multiplication (dot product, cross product) that aren't included in this calculator.

Q4: Are the results unitless?
A: The results will have the same units as the input vectors. If your vectors represent physical quantities, include appropriate units.

Q5: Can I add more than two vectors?
A: This calculator only handles two vectors at a time. For multiple vectors, you would need to perform operations sequentially.