Vectors in Space
Interactive exploration of vector addition and direction
Explore vector operations in 3D space by adjusting vector components and observing how they add together. Visualize vector addition, subtraction, and scalar multiplication in real-time!
Vector A
Vector B
Vector Operations:
Dot Product (A·B): 1.5
Angle between A and B: 75.5°
Magnitude of A: 2.29
Magnitude of B: 2.69
Current Operation:
Vector addition combines two vectors tip-to-tail. The resultant vector goes from the tail of the first to the tip of the second vector.
A + B = (Aₓ+Bₓ, Aᵧ+Bᵧ, A_z+B_z)
Understanding Vectors in Space
Key Concepts:
Vectors are quantities with both magnitude and direction:
- Components: Vectors can be broken down into x, y, z components
- Magnitude: Length of the vector (calculated using Pythagorean theorem)
- Direction: Orientation in space (often represented by angles or unit vectors)
- Operations: Vectors can be added, subtracted, and multiplied in special ways
Vector Operations:
- Addition: Combine vectors tip-to-tail
- Subtraction: Reverse one vector and add
- Dot Product: Measures parallelness (scalar result)
- Cross Product: Measures perpendicularity (vector result)
