Unit Tangent Vector Calculator
What is Unit Tangent Vector?
A unit tangent vector is the derivative of a vector-valued function that provides another vector-valued function unit tangent to the defined curve. It represents the direction of motion along a curve at any given point. The unit tangent vector is obtained by normalizing the velocity vector (derivative of the position vector) by dividing it by its magnitude. This process ensures the resulting vector has a magnitude of 1 while maintaining the direction of motion.
How to Calculate Unit Tangent Vector
Step 1: Enter your vector-valued function r(t) in component form
Step 2: Input the specific point t where you want to find the unit tangent vector.
Step 3: Click the “Calculate” button to obtain the derivative r'(t).
Step 4: Review the normalized result T(t) = r'(t)/||r'(t)||.
Step 5: Examine the step-by-step solution showing the derivative calculation and normalization process.
Step 6: Verify the final unit tangent vector components and magnitude.