Vector Calculator 3 Vectors

Vector Sum Equation:

\[ \vec{R} = \vec{A} + \vec{B} + \vec{C} \]

Vector A

X component:

Y component:

Z component:

Vector B

X component:

Y component:

Z component:

Vector C

X component:

Y component:

Z component:

Resultant Vector (R):

Magnitude:

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1. What is Vector Addition?

Vector addition is the operation of combining two or more vectors into a single vector called the resultant. In physics and engineering, this is essential for understanding forces, velocities, and other vector quantities.

2. How Does the Calculator Work?

The calculator uses component-wise addition:

\[ \vec{R} = \vec{A} + \vec{B} + \vec{C} = (A_x+B_x+C_x)\hat{i} + (A_y+B_y+C_y)\hat{j} + (A_z+B_z+C_z)\hat{k} \]

Where:

\( \vec{A}, \vec{B}, \vec{C} \) — Input vectors
\( \vec{R} \) — Resultant vector
\( A_x, A_y, A_z \) — Components of vector A
\( \hat{i}, \hat{j}, \hat{k} \) — Unit vectors in x, y, z directions

3. Applications of Vector Addition

Physics: Calculating net force, combining velocities, analyzing electric fields.
Engineering: Structural analysis, fluid dynamics, robotics.
Computer Graphics: Object movement, lighting calculations.

4. Using the Calculator

Instructions: Enter the x, y, z components for each vector. The calculator will compute the resultant vector and its magnitude.

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: How is the magnitude calculated?
A: Magnitude = √(R_x² + R_y² + R_z²)

Q3: Can I add more than 3 vectors?
A: Yes, by adding vectors two at a time or by extending the formula for more vectors.

Q4: What if I only have 2D vectors?
A: Simply set the z-components to zero.

Q5: Does order of addition matter?
A: No, vector addition is commutative (A+B+C = C+B+A).