Find out general formula for tangent vector and unit vector, Mathematics

Assignment Help:

Find out the general formula for the tangent vector and unit tangent vector to the curve specified by

r (t) = t2 i + 2 sin t j + 2 cos t k.

Solution

First, by common formula we mean that we won't be plugging in a particular t and thus we will be finding out a formula that we can utilize at a later date if we would like to find the tangent at any point on the curve.  Along with that said there really isn't all that much to do at this point other than to do the work.

Here below is the tangent vector to the curve.

r′ (t) = 2t i  + 2 cos t j - 2 sin t k

To obtain the unit tangent vector we require the length of the tangent vector.

|| r′ (t)|| = √ (4t2 + 4cos2 t + 4 sin2 t)

= √ (4t2 + 4)

After that the unit tangent vector is,

524_Find out general formula for tangent vector and unit vector.png


Related Discussions:- Find out general formula for tangent vector and unit vector

Area with parametric equations - polar coordinates, Area with Parametric Eq...

Area with Parametric Equations In this section we will find out a formula for ascertaining the area under a parametric curve specified by the parametric equations, x = f (t)

NCCER, what is 9/16 Divided by 7/8

what is 9/16 Divided by 7/8

Matrices, problem faced by students

problem faced by students

Sets, creative assignment about sets

creative assignment about sets

Calculate the volume of rectangular piece of cardboard, 1. A rectangular pi...

1. A rectangular piece of cardboard measuring 15 inches by 24 inches is to be made into a box with an open top by cutting equal size squares from each comer and folding up the side

Proof of sum-difference of two functions, Proof of Sum/Difference of Two Fu...

Proof of Sum/Difference of Two Functions : (f(x) + g(x))′  = f ′(x) +  g ′(x)  It is easy adequate to prove by using the definition of the derivative.  We will start wi

Formula to know the area of fan will wrap, Aaron is installing a ceiling fa...

Aaron is installing a ceiling fan in his bedroom. Once the fan is in motion, he requires to know the area the fan will wrap. What formula will he use? The area of a circle is π

Boat Crossing, What is the slowest a boat can travel across a river if the ...

What is the slowest a boat can travel across a river if the river is flowing with a velocity field of X^2?

Fractions, my daughter brought home home work im not sure how to do it the ...

my daughter brought home home work im not sure how to do it the fractions has to be labled from least to greatest

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