Tangent,normal and binormal vector - three dimensional space, Mathematics

Assignment Help:

Tangent, Normal and Binormal Vectors

In this part we want to look at an application of derivatives for vector functions.  In fact, there are a couple of applications, but they all come back to requiring the first one.

In the past we have employed the fact that the derivative of a function was the slope of the tangent line. Along with vector functions we obtain exactly similar result, along with single exception.

There is a vector function, r (t) , we call r′ (t) the tangent vector specified by it exists and provided r′ (t) ≠ 0 . After that the tangent line to r (t) at P is the line that passes via the point P and is parallel to the tangent vector, r′ (t). 

Notice: we really do need to require r?′ (t) ≠ 0 to have a tangent vector.  Whether we had r′(t) = 0we would have a vector that had no magnitude and thus could not give us the direction of the tangent.


Related Discussions:- Tangent,normal and binormal vector - three dimensional space

Inequalities, seven more than a number is less than or equal to -18

seven more than a number is less than or equal to -18

Fraction, give some examples of fractions that are already reduce

give some examples of fractions that are already reduce

Pre Calc, Find reference angle alpha and thea element of [0 degrees, 1800 d...

Find reference angle alpha and thea element of [0 degrees, 1800 degrees]

Prepare a bar diagram, Question Write a short note on the following: ...

Question Write a short note on the following: 1 The weekly salaries of a group of employees are given in the following table. Find the mean and standard deviation of the

Geometry, prove angle MJL is congruent to angle KNL

prove angle MJL is congruent to angle KNL

Example of the invisible effort, Imagine a time in history when the number ...

Imagine a time in history when the number system had not yet evolved a farmer needed to keep track of his cattle. What would he do to figure out whether his entire rattle returned

Product moment coefficient (r), Product Moment Coefficient (r) ...

Product Moment Coefficient (r) This gives an indication of the strength of the linear relationship among two variables.                                     N

Standardization of variables, Standardization of Variables - Before we...

Standardization of Variables - Before we use the general distribution curve to determine probabilities of the continuous variables, we require standardizing the original units

Matrices, Give me the assignment on the matrices...

Give me the assignment on the matrices...

Greatest common factor, x 4 - 25 There is no greatest common factor her...

x 4 - 25 There is no greatest common factor here.  Though, notice that it is the difference of two perfect squares. x 4 - 25 = ( x 2 ) 2   - (5) 2 Thus, we can employ

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd