1. What is Vector Addition?

Vector addition is the operation of adding two or more vectors together into a vector sum. The resulting vector is obtained by adding corresponding components of the vectors.

2. How Does the Calculator Work?

The calculator uses the vector addition formula:

Where:

• \( A \) — First vector with components (A_x, A_y, A_z)
• \( B \) — Second vector with components (B_x, B_y, B_z)
• \( V \) — Resultant vector

Explanation: The calculator simply adds the corresponding x, y, and z components of the two vectors to produce the resultant vector.

3. Importance of Vector Addition

Details: Vector addition is fundamental in physics and engineering for combining forces, velocities, accelerations, and other vector quantities. It's essential for analyzing systems with multiple interacting components.

4. Using the Calculator

Tips: Enter all components of both vectors. The calculator supports 3-dimensional vectors. For 2D vectors, simply leave the z-components as 0.

5. Frequently Asked Questions (FAQ)

Q1: Can I add more than two vectors?
A: This calculator adds two vectors. For more vectors, you would need to add them sequentially two at a time.

Q2: What's the difference between vector and scalar addition?
A: Vector addition considers both magnitude and direction, while scalar addition only considers magnitude.

Q3: How is vector addition represented graphically?
A: The "tip-to-tail" method places the tail of the second vector at the tip of the first vector. The resultant goes from the tail of the first to the tip of the second.

Q4: Does vector addition follow commutative law?
A: Yes, A + B = B + A for vector addition.

Q5: What about vector subtraction?
A: Subtraction is simply adding the negative of a vector (A - B = A + (-B)).