Vector Mission Control
Explore vector operations and visualizations
- Represent vectors in component form and calculate magnitude
- Perform vector addition, subtraction, and scalar multiplication
- Calculate dot product and understand its geometric meaning
- Find the angle between two vectors
v =
a
i +
b
j
A vector has both magnitude and direction. In 2D, v = ai + bj where a is the horizontal component and b is the vertical component. The magnitude |v| = √(a² + b²) is the length. The dot product u·v = |u||v|cos(θ) gives the angle between vectors. Vectors are fundamental in physics for forces, velocities, and displacements.
Goal: Define two vectors, perform operations, and see the results on the 2D plane.
Real-World: Pilots use vectors for navigation, game developers for character movement, engineers for force calculations.
Vector u
Enter components for two vectors. A vector has both magnitude (how long) and direction (which way) — unlike a plain number which only has size.
Vector v
Enter components for the second vector to perform operations between u and v.
Operation
Choose an operation to see it visually. Addition places vectors tip-to-tail, the dot product measures how aligned two vectors are, and the cross product finds a vector perpendicular to both.
Vector Information
The graph shows vectors as arrows from the origin. Magnitude and angle information updates as you adjust components.
|u| = 0
|v| = 0
Angle between u and v: 0°
Operation Result
The result updates instantly. Notice how the dot product gives a single number (scalar) while the cross product gives a new vector — they answer different geometric questions.