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. Importance of Vector Addition

Details: Vector addition is fundamental in physics and engineering for combining forces, velocities, and other vector quantities. It's essential for understanding motion, electromagnetism, and structural analysis.

4. Using the Calculator

Tips: Enter the x, y, and z components for both vectors. The calculator will compute the sum of corresponding components. You can use positive or negative values as needed.

5. Frequently Asked Questions (FAQ)

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

Q2: Can I add vectors of different dimensions?
A: No, vectors must have the same number of components to be added.

Q3: What is the geometric interpretation of vector addition?
A: The sum vector is the diagonal of the parallelogram formed by the two vectors (parallelogram law).

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

Q5: How is vector subtraction related to addition?
A: Vector subtraction is equivalent to adding the negative of a vector (a - b = a + (-b)).