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

Examining a related problem, how to explain this strategy? how to do this s...

how to explain this strategy? how to do this strategy in solving a problem? can you give some example on how to solve this kind of strategy.

Poisson mathematical properties, Poisson Mathematical Properties 1. Th...

Poisson Mathematical Properties 1. The expected or mean value = np = λ Whereas; n = Sample Size p = Probability of success 2. The variance = np = ? 3. Standard dev

Probability, an insurance salesman sells policies to 5 men, all of identica...

an insurance salesman sells policies to 5 men, all of identical age in good health. the probability that a man of this particular age will be alive 20 years hence is 2/3.Find the p

upper and lower limits, A critical dimension of the service quality of a c...

A critical dimension of the service quality of a call center is the wait time of a caller to get to a sales representative. Periodically, random samples of 6 customer calls are mea

Algebra 1A, The m&m factory produces 2,500 packs of plain m&ms each day. R...

The m&m factory produces 2,500 packs of plain m&ms each day. Represent the total number of packs of plain m&ms the factory makes each day

Absolute value, Consider x € R. Then the magnitude of x is known as it's...

Consider x € R. Then the magnitude of x is known as it's absolute value and in general, shown by |x| and is explained as Since the symbol   always shows the nonnegative

Statistics, How many 4 digit numbers can be formed using the numbers: 1 – 7...

How many 4 digit numbers can be formed using the numbers: 1 – 7. Repeated numbers CAN NOT be used

Partial Differential Equation, Determine the minimum capacity C of a Capaci...

Determine the minimum capacity C of a Capacitor given that: C =(ax/(x-a))+(xy/(y-b))+(yb/(b-y)) given that "a" and "b" are fixed values and "x" and "y" vary independently such th

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