Vector function - three dimensional spaces, Mathematics

Assignment Help:

Vector Function

The good way to get an idea of what a vector function is and what its graph act like is to look at an instance.  Thus, consider the following vector function.

874_Vector Function - Three dimensional spaces 3.png

A vector function is a function which takes one or more variables, one in this case, and returns a vector.  Note also that a vector function can be a function of two or more than two variables.  Though, in those cases the graph might no longer be a curve in space.

The vector that the function provides can be a vector in whatever dimension we require it to be.  In the instance above it returns a vector in R2.  While we get to the real subject of this section, equations of lines, we will be using a vector function which returns a vector in R3.

Here now, we want to find out the graph of the vector function above.  To find the graph of our function we'll think of the vector that the vector function returns like a position vector for points on the graph.  Remind that a position vector, say, ¯v = (a,b) is a vector that begins at the origin and ends at the point  (a,b).  

 Thus, to get the graph of a vector function all we require to do is plug in some values of the variable and after that plot the point that corresponds to each position vector we get out of the function and play connect the dots.  Now here are some evaluations for our instance.

603_Vector Function - Three dimensional spaces 2.png

Thus, each of these are position vectors presenting points on the graph of our vector function.  The points,

are all points that lie on the graph of our vector function. 

If we do some other evaluations and plot all the points we obtain the subsequent sketch.

28_Vector Function - Three dimensional spaces 1.png

In this diagram we've included the position vector (in gray and dashed) for various evaluations also the t (above each point) we employed for each evaluation.  It looks like, in this case the graph of the vector equation is in fact the line  y =1.


Related Discussions:- Vector function - three dimensional spaces

Determine the probability - probability example, Consider two bags, A and B...

Consider two bags, A and B, with the following contents Bag A Bag B 3 white marbles 4 white marbles 2 red marbles

Geometry, a figure is made of a rectangle and an isosceles right triangle. ...

a figure is made of a rectangle and an isosceles right triangle. the rectangle has sides of 6 in. and 3 in. one of the short sides of the rectangle is also one of the legs of the r

Pair of straight lines, how to solve the problems? methods to solve the que...

how to solve the problems? methods to solve the question of joint lines

Triangle Treat, Triangle Treat is the page name. I don''t know the answer f...

Triangle Treat is the page name. I don''t know the answer for it, can someone give it to me?

Fundamentals of math, When there are 4 dots how many chords are they

When there are 4 dots how many chords are they

If the area of the parallelogram is 36 m2 what is the height, The height of...

The height of a parallelogram measures 5 meters more than its base. If the area of the parallelogram is 36 m 2 , what is the height in meters? Let x = the measure of the base a

Determine the team having similar code-pigeon hole principle, Shirts number...

Shirts numbered consecutively from 1 to 20 are worn by 20 members of a bowling league. While any three of these members are selected to be a team, the league aims to use the sum of

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