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

Rhjuu, Ask questutfjion #Minimum 100 words accepted#

Ask questutfjion #Minimum 100 words accepted#

Expressions, how do you solve expressions

how do you solve expressions

Expert , i want to work with you, please guide me

i want to work with you, please guide me

Statistic, Suppose that the probability of your favorite baseball player ge...

Suppose that the probability of your favorite baseball player getting a hit at bat is 0.45. Assume that each at bat is independent. What is the probability that he bats eight times

High dimensions, List the five most important things you learned about high...

List the five most important things you learned about high dimensions.

Applying percents, If a single person makes $25,00 a year, how much federal...

If a single person makes $25,00 a year, how much federal income tax will he or she have to pay ?And they are gining me a chart that says $0 to $27,050 is 15% of taxes .

Speed, Town x and town y were 270km apart. a car started from town x toward...

Town x and town y were 270km apart. a car started from town x towards town y at a uniform speed of 60km/hr, while a motorcycle started from town y to town x at a uniform speed of 9

What is the meaning of the f-statistic and f test, You are given the follow...

You are given the following regression results estimating the demand for widgets based on time series data for the past 40 months. Q t = 2.5 - 0.3 x P t + 12 x M t Where Q

Derivatives, Derivatives The rate of change in the value of a...

Derivatives The rate of change in the value of a function is useful to study the behavior of a function. This change in y for a unit change in x is

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