Quadratic Equation Solver (ax² + bx + c = 0)
About Vector Calculator
The 2D & 3D Vector Geometry & Kinematics Calculator computes vector magnitude ($||\vec{v}||$), unit direction vectors ($\hat{v}$), vector addition/subtraction ($\vec{u} \pm \vec{v}$), scalar multiplication, dot/cross products, and angles between vectors ($\theta$).
How to Use Vector Calculator
Step 1
Select vector dimension (2D, 3D, or N-D).
Step 2
Enter components for Vector A and Vector B.
Step 3
Select operation (Resultant, Magnitude, Dot/Cross Product, or Angle).
Step 4
Inspect 3D graphical vector plot and copy mathematical solutions.
Practical Use Cases for Vector Calculator
Game Development & 3D Physics Simulation
Normalize character velocity vectors and compute surface normal reflection angles for 3D game physics engines.
Mechanical Engineering Force Vectors & Statics Equilibrium
Calculate resultant force magnitudes and directional cosines for structural trusses and tension cables.
Input & Output Examples
Analyzing 3D Vector Operations
Vector u: `[3, 4, 0]`, Vector v: `[1, 2, 2]`
||u|| = `5.0` | ||v|| = `3.0` | Dot Product: `11` | Angle: `42.83°` | Cross Product: `[8, -6, 2]`
Key Features & Performance
- ✓Computes: Vector Norm / Magnitude, Unit Vector ($\vec{v}/||\vec{v}||$), Direction Angles ($\alpha, \beta, \gamma$), Dot Product, Cross Product.
- ✓Supports 2D ($x, y$), 3D ($x, y, z$), and arbitrary N-Dimensional vector spaces.
- ✓Interactive 2D/3D Canvas vector plot with live rotational camera controls.
- ✓100% Client-Side vector geometry engine.
- ✓1-Click Copy vector components & LaTeX notation.
Key Terminology & Definitions
Unit Vector ($\hat{v}$)
A vector of length 1 pointing in the identical direction as the original vector, computed as $\vec{v} / ||\vec{v}||$.
Euclidean Norm ($||\vec{v}||$)
The straight-line length of a vector from origin to tip, calculated via the Pythagorean distance formula $\sqrt{\sum v_i^2}$.