High School Vector Calculator
Calculate Dot Product, Cross Product, and visualize in 3D
Vector A (Blue)
Vector B (Red)
3D Visualization
Dot Product (Scalar)
0
Formula: A · B
Cross Product (Vector)
(0, 0, 12)
Formula: A × B
Angle (θ)
90°
Between vectors
Magnitudes
Understanding Vectors
Welcome to the Vector Calculator. In physics and math, a vector is like an arrow: it has a length (magnitude) and points in a specific direction. Regular numbers are just “scalars” (size only), but vectors are more dynamic.
1. The Dot Product
Think of this as the “Shadow Product”. It tells you how much of one vector is pushing in the same direction as the other.
- Result is a Number.
- Used for calculating work done or checking alignment.
- A · B = 0 means they are perpendicular (90°).
2. The Cross Product
This creates a brand new vector that sticks straight out, perpendicular to both original vectors.
- Result is a Vector (Green arrow).
- Used for torque, rotation, and magnetic fields.
- Direction follows the “Right-Hand Rule”.
Quick FAQ
Why is the result 0?
For Dot Product: The vectors are perpendicular (90°).
For Cross Product: The vectors are parallel (pointing same or opposite way).
What is the “Right-Hand Rule”?
If you point your index finger along Vector A and middle finger along Vector B, your thumb points in the direction of the Cross Product.