Resultant Vector Calculator

Calculate resultant vector magnitude, direction, and components in 2D and 3D space. Perfect for physics, engineering, and mathematics applications.

2D Vector Input

Add multiple vectors and calculate their resultant.

Vector	X-comp	Y-comp	Magnitude	Angle (°)	Action
V1

Resultant Vector (2D)

R = 3.00î + 4.00ĵ

Magnitude

5.00

Direction

53.13°

X-component

3.00

Y-component

4.00

Formula: R = √(Σx² + Σy²)
Direction: θ = tan⁻¹(Σy/Σx)

Vector Diagram

• Resultant magnitude: 5.00 units
• Direction from x-axis: 53.13°
• Quadrant: I

Vector Mathematics Guide

Vector Fundamentals

A vector has both magnitude and direction. Key concepts:

Magnitude: Length of the vector
Direction: Orientation in space
Components: Projections on coordinate axes
Resultant: Sum of multiple vectors
Unit Vector: Vector with magnitude 1

2D Vector: v = xî + yĵ
3D Vector: v = xî + yĵ + zk̂

Applications & Real-World Uses

Physics: Force analysis, motion, electromagnetism

Engineering: Structural analysis, mechanics, robotics

Computer Graphics: 3D modeling, game development, animations

Navigation: GPS, aircraft guidance, ship routing

Mathematics: Linear algebra, geometry, optimization

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