Determine the unit tangent vector

In summary, a unit tangent vector is a vector that is tangent to a curve and has a magnitude of 1. It can be calculated by taking the derivative of the position vector of the curve and dividing it by its magnitude. The unit tangent vector is important because it helps us understand the direction of a curve at a specific point and is useful in calculating other important quantities. It is also related to the normal vector, which is found by taking the cross product of the unit tangent vector and the unit binormal vector. The main difference between a unit tangent vector and a regular tangent vector is that a unit tangent vector has a fixed magnitude and represents the direction of the curve at a specific point, while a regular tangent vector does not have a fixed
  • #1
chwala
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Homework Statement
see attached
Relevant Equations
vector differentiation
1644910436015.png


I need a justification that ##|\dfrac {dr}{dt}|##=##\dfrac {ds}{dt}## cheers guys... all the other steps are easy and clear to me...
 
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  • #2
chwala said:
Homework Statement:: see attached
Relevant Equations:: vector differentiation

View attachment 297138

I need a justification that [Modulus ##\big | \dfrac {dr}{dt} \big |##=##\dfrac {ds}{dt}##] cheers guys... all the other steps are easy and clear to me...
We have ##ds \equiv |d\vec r|##.
 
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Aaaaah Perok cheers!
PeroK said:
We have ##ds \equiv |d\vec r|##.
 

FAQ: Determine the unit tangent vector

What is a unit tangent vector?

A unit tangent vector is a vector that is tangent to a curve at a specific point and has a magnitude of 1. It represents the direction and rate of change of the curve at that point.

How is the unit tangent vector calculated?

The unit tangent vector is calculated by taking the derivative of the curve at the given point and then normalizing the resulting vector to have a magnitude of 1.

What is the significance of the unit tangent vector?

The unit tangent vector is important in understanding the behavior of a curve at a specific point. It can be used to determine the direction of the curve and the rate of change at that point.

Can the unit tangent vector change along a curve?

Yes, the unit tangent vector can change along a curve as the direction and rate of change of the curve may vary at different points. It is a function of the derivative of the curve at each point.

How is the unit tangent vector used in real-world applications?

The unit tangent vector is used in many fields such as physics, engineering, and computer graphics. It can help determine the direction and acceleration of moving objects, the curvature of a path, and the orientation of a shape in 3D space.

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