1. What is Vector Addition?

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

2. How Does the Calculator Work?

The calculator uses the vector addition formula:

Where:

• \( \vec{a} \) — First vector with components (aₓ, aᵧ, a_z)
• \( \vec{b} \) — Second vector with components (bₓ, bᵧ, b_z)
• \( \vec{sum} \) — Resultant vector

Explanation: Each component of the resulting vector is the algebraic sum of the corresponding components of the original vectors.

3. Applications of Vector Addition

Details: Vector addition is fundamental in physics (forces, velocities), engineering, computer graphics, and navigation. It's used to calculate net forces, combined velocities, and resultants of multiple influences.

4. Using the Calculator

Tips: Enter the x, y, and z components for both vectors. The calculator will compute the sum vector component-wise. For 2D vectors, simply enter 0 for the z-component.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between vector and scalar addition?
A: Vector addition considers both magnitude and direction (component-wise), while scalar addition only involves magnitudes.

Q2: Can I add more than two vectors?
A: Yes, vector addition is associative - you can add vectors two at a time in any order.

Q3: What's the geometric interpretation?
A: The sum vector is the diagonal of the parallelogram formed by the two vectors (head-to-tail method).

Q4: Does vector addition commute?
A: Yes, vector addition is commutative: a + b = b + a.

Q5: How to handle negative components?
A: Negative components represent opposite directions. The calculator handles them correctly in the addition.