V1 V2 Vector Calculator

Vector Addition Formula:

\[ \vec{v1} + \vec{v2} = \langle v1_x + v2_x, v1_y + v2_y, v1_z + v2_z \rangle \]

Vector 1 X-component:

Vector 1 Y-component:

Vector 1 Z-component:

Vector 2 X-component:

Vector 2 Y-component:

Vector 2 Z-component:

Vector Sum (v1 + v2):

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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:

\[ \vec{v1} + \vec{v2} = \langle v1_x + v2_x, v1_y + v2_y, v1_z + v2_z \rangle \]

Where:

\( \vec{v1} \) — First vector with components (x, y, z)
\( \vec{v2} \) — Second vector with components (x, y, z)
The result is a new vector where each component is the sum of the corresponding components

3. Applications of Vector Addition

Details: Vector addition is fundamental in physics, engineering, computer graphics, and many other fields where quantities have both magnitude and direction.

4. Using the Calculator

Tips: Enter the components of both vectors. The calculator will compute the resulting vector by adding corresponding components.

5. Frequently Asked Questions (FAQ)

Q1: Does vector addition commute?
A: Yes, vector addition is commutative: v1 + v2 = v2 + v1.

Q2: What's the geometric interpretation?
A: The sum vector can be visualized as the diagonal of the parallelogram formed by the two vectors.

Q3: Can I add vectors of different dimensions?
A: No, vectors must have the same number of components to be added.

Q4: What about vector subtraction?
A: Subtraction is similar but you subtract corresponding components instead of adding them.

Q5: How is this different from scalar addition?
A: Scalar addition is just regular number addition, while vector addition operates on multiple components simultaneously.