Vector Calculations
Understanding vectors, their operations, and the geometric meaning behind the scalar (dot) product
What is a Vector?
A vector is a mathematical object that has both magnitude (length) and direction.
In 2D, a vector v can be written as:
v = (vx, vy) or v = vxi + vyj
Where:
- vx is the horizontal component
- vy is the vertical component
- i and j are unit vectors along x and y axes
Magnitude of a Vector
|v| = √(vx² + vy²)
Interactive Vector Visualization
Drag the points to see how vector components change:
Interactive visualization — available in the full lesson
Vector Operations
Addition
u + v = (ux + vx, uy + vy)
Add corresponding components
Subtraction
u - v = (ux - vx, uy - vy)
Subtract corresponding components
Scalar Multiplication
kv = (kvx, kvy)
Multiply each component by scalar k