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

The central limit theorem, The Central Limit Theorem  The theories was ...

The Central Limit Theorem  The theories was introduced by De Moivre and according to it; if we choose a large number of simple random samples, says from any population and find

Triangle and its properties, in a triangle angle a is 70 and angle b is 50 ...

in a triangle angle a is 70 and angle b is 50 what is angle c.

Matrix, find the matrix of the linear transformations T:R2->R2 defined by T...

find the matrix of the linear transformations T:R2->R2 defined by T(x,y,z)=(x+2y,x-3z).

Curve tracing, how to curve trace? and how to know whether the equation is ...

how to curve trace? and how to know whether the equation is a circle or parabola, hyperbola ellipse?

Areas related to circles in mensuration, AREAS  RELATED TO CIRCLES The...

AREAS  RELATED TO CIRCLES The  mathematical  sciences particularly  exhibit  order,  symmetry,  and limitation;  and  these  are the  greatest  forms  of the beautiful. In t

Math.., how many sixs are in 60

how many sixs are in 60

Trigonometric ratios, to difine trigonometric ratios of an angle,is it nece...

to difine trigonometric ratios of an angle,is it necessary that the initial ray of the angle must be positive x-axis?

Differential equations and group methods, solve the differential equation ...

solve the differential equation dy/dx=f(y)x^n+g(y)x^m by finding a one-parameter group leaving it invariant

Numerical analysis, Please,I Want to know and study for stability on predi...

Please,I Want to know and study for stability on predictor -corrector for numerical integration method

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