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

Complex, find all the 8th roots of (19+7i)

find all the 8th roots of (19+7i)

Cylinder, #question Show that the enveloping cylinder of the conicoid ax 2 ...

#question Show that the enveloping cylinder of the conicoid ax 2 + by 2 + cz 2 = 1 with generators perpendicular to the z-axis meets the plane z = 0 in parabolas

Probability, Probability -Probability is an extremely popular concept ...

Probability -Probability is an extremely popular concept in business management. Since it covers the risks such may be included in certain business situations. This is a fact

Estimation of difference among two means, Estimation of difference among tw...

Estimation of difference among two means We know that the standard error of a sample is given by the value of the standard deviation (σ) divided by the square root of the numbe

Develop a linear algebraic equation, Introduction: "Mathematical liter...

Introduction: "Mathematical literacy is an individual's capacity to identify and understand the role that mathematics plays in the world, to make well-founded judgments, and t

Testing the difference between two sample means-illustration, An observatio...

An observation was made concerning reading abilities of males and females. The observation leads to a conclusion that females are faster readers than males. The observation was bas

Geometry, P and Q are the points (12,0) and (0,-5) respectively,find the le...

P and Q are the points (12,0) and (0,-5) respectively,find the length of the median through the origin O of the triangle OPQ

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