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Mathematics
Vector addition and components
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vector b= (15; 4)
Display layers
Move the origin
Moving O changes the coordinates of the points, not the components.
- x component
- (−6) + 15 = 9
- y component
- 8 + 4 = 12
- Magnitude
- |vector s| = √(9² + 12²) = 15
- Angle with Ox
- 53.13°
Moving a vector preserves its components. Moving the tip changes its length or direction and can change the sum.
Model notes
- Vectors represent mathematical quantities, not moving particles. Their length and direction determine the components; moving a whole vector does not change the sum.
- Cartesian vectors snap to integer grid coordinates. Polar lengths snap to integers and angles to 5° increments. Only vectors on the graph contribute to the sum.
- The 1D and 2D scenes keep separate configurations. The tip-to-tail construction moves copies of positions without changing components. The zero resultant has no defined direction.