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

Determine the function notation, Given f (x) = - x 2 + 6 x -11 determine e...

Given f (x) = - x 2 + 6 x -11 determine each of the following. (a)    f ( 2) (b)   f ( -10) (c)    f (t ) Solution (a)    f ( 2) = - ( 2) 2   + 6(2) -11 = -3 (

Mensuration, a hollow cone is cut by a plane parallel to the base and the u...

a hollow cone is cut by a plane parallel to the base and the upper portion is removed. if the volume of the frustum obtained is 26/27 of volume of the cone. find at what height abo

Volume, Rajun uses 2/3 of a carton of milk to make a pancake. The volume of...

Rajun uses 2/3 of a carton of milk to make a pancake. The volume of milk he uses is 800ml. calculate the volume, in l, of a milk in carton?

Prove that r is an equivalence relation, 1. Let S be the set of all nonzero...

1. Let S be the set of all nonzero real numbers. That is, S = R - {0}. Consider the relation R on S given by xRy iff xy > 0. (a) Prove that R is an equivalence relation on S, an

Interpretation of the second derivative, Interpretation of the second deriv...

Interpretation of the second derivative : Now that we've discover some higher order derivatives we have to probably talk regarding an interpretation of the second derivative. I

..percentage, how to express 15/4 into percentage

how to express 15/4 into percentage

Discount, outdoor grill- regular price:$360 discount:33 1/3%

outdoor grill- regular price:$360 discount:33 1/3%

Determine principal strains and direction , A 100 by 150 mm rectangular pla...

A 100 by 150 mm rectangular plate is deformed as shown in the following figure. All dimensions shown in the figure are in millimeters.  Determine at point Q: (a) the strain compone

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