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 performs vector addition using the following formula:

Where:

• \( \vec{a} \) — First vector with components (a_x, a_y, a_z)
• \( \vec{b} \) — Second vector with components (b_x, b_y, b_z)
• \( \vec{v}_{result} \) — Resultant vector

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

3. Applications of Vector Addition

Details: Vector addition is fundamental in physics, engineering, computer graphics, and navigation. It's used to calculate forces, velocities, and displacements in multiple dimensions.

4. Using the Calculator

Tips: Enter the x, y, and z components for both vectors. The calculator will compute and display the resultant vector. All fields are required.

5. Frequently Asked Questions (FAQ)

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

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

Q3: What if I only have 2D vectors?
A: Simply enter 0 for the z-component to use this calculator with 2D vectors.

Q4: How is vector addition represented graphically?
A: Graphically, vectors are added using the "tip-to-tail" method or parallelogram method.

Q5: Can this calculator perform other vector operations?
A: This version only performs vector addition, but could be extended to include subtraction, dot product, and cross product.