Unit Tangential and Normal Vectors calculation
- Author:
- washu
Unit Tangential and Normal Vectors calculation.
It shows the exact formula used to calculate those vectors for a given curve (not using geogebra built-in functions).
May be difficult to visualize the formulas inside geogebra but it's basically the following: The Unit Tangent Vector is simply the velocity vector over its magnitude, the Unit Normal Vector is the derivative of the Unit Tangent Vector over its magnitude. And to understand why this results in the normal vector intuitively is quite simple, since the only change that happens in the Unit Tangent Vector is in its angle and never in its magnitude (which is always 1) the direction of the resulting vector is always at a right angle to the Unit Tangent Vector, this resulting vector is then divided by its magnitude giving you the Unit Normal Vector.