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

Harmonic mean, If a, b and c are in harmonic progression with b as th...

If a, b and c are in harmonic progression with b as their harmonic mean then, b  = This is obtained as follows. Since a, b and c are in

Rationalize the denominator, Rationalize the denominator for following.  Su...

Rationalize the denominator for following.  Suppose that x is positive. Solution We'll have to start this one off along with first using the third property of radica

Calculus, Calculus Calculus is a branch of mathematics which describes...

Calculus Calculus is a branch of mathematics which describes how one variable changes in relationship to another variable. It enables us to determine the rate of change of one

Find the area of the shaded region, ABC is a right angled triangle in which...

ABC is a right angled triangle in which ∠A = 900. Find the area of the shaded region if AB = 6 cm, BC=10cm & I is the centre of the Incircle of ?ABC. Ans: ∠A =90 0 BC

Example on abels theorem, Without solving, find out the Wronskian of two so...

Without solving, find out the Wronskian of two solutions to the subsequent differential equation. t 4 y'' - 2t 3 y' - t 8 y = 0 Solution : First thing that we want to d

Probability, One coin is tossed thrice. what will be the probability of get...

One coin is tossed thrice. what will be the probability of getting neither 3 heads nor 3 tails

.fractions, what is the difference between North America''s part of the tot...

what is the difference between North America''s part of the total population and Africa''s part

Communicating the meaning of addition, COMMUNICATING THE MEANING OF ADDITIO...

COMMUNICATING THE MEANING OF ADDITION :  One of the characters in a novel written by the Malayalam writer Vaikom Muhammed Basheer was asked by his teacher, "How much is one and on

., Two boys A and B are at two diametrically opposite points on a circle. A...

Two boys A and B are at two diametrically opposite points on a circle. At one instant the two start running on the circle; A anticlockwise with constant speed v and B clockwise wit

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