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

Simultaneous equations, two rolls of carpet cost £574, the first cost £8 pe...

two rolls of carpet cost £574, the first cost £8 per meter, the second which is 7m longer costs £7 p/m. how many meters are there in each roll

Taylor series - sequences and series, Taylor Series - Sequences and Series ...

Taylor Series - Sequences and Series In the preceding section we started looking at writing down a power series presentation of a function.  The difficulty with the approach

Adding fractions with the same denominator, Q. Adding Fractions with the Sa...

Q. Adding Fractions with the Same Denominator? Adding fractions with the same denominator is easy- you add the numerators (the tops), and you leave the denominator alone!

Math 533, Project part A, part B, part C

Project part A, part B, part C

Draw the digraph for the partial order, 1. Consider the relation on A = {1,...

1. Consider the relation on A = {1, 2, 3, 4} with relation matrix: Assume that the rows and columns of the matrix refer to the elements of A in the order 1, 2, 3, 4. (a)

Work Word Problems, Data entry is performed in 2-person teams. Each 2-perso...

Data entry is performed in 2-person teams. Each 2-person team can enter 520 surveys per day. A selection of 7540 surveys must be entered by day''s end. How many total employees, wo

Determine the circumference, If Gretta's bicycle has a 25-inch radius wheel...

If Gretta's bicycle has a 25-inch radius wheel, how far will she travel in two turns of the wheel? (π = 3.14) a. 491 in b. 78.5 in c. 100 in d. 157 in d. To determin

Trigonometry identity, if x+y+z=pi=180 prove that sin^2x+sin^2y+sin^z-2sinx...

if x+y+z=pi=180 prove that sin^2x+sin^2y+sin^z-2sinx*siny*sinz=2

If a sequence is bounded and monotonic then it is convergent, Theorem ...

Theorem If {a n } is bounded and monotonic then { a n } is convergent.  Be cautious to not misuse this theorem.  It does not state that if a sequence is not bounded and/or

Accuray and Precision, If an instrument has precision of +-1, can it detect...

If an instrument has precision of +-1, can it detect a value of 1.3?

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