{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ch13sec1

# ch13sec1 - 13.1 Vector Functions and Space Curves We have...

This preview shows pages 1–2. Sign up to view the full content.

13.1 Vector Functions and Space Curves We have studied functions, , that represent the position of a particle on a line. This notion can be extended to more than 1 dimension. Two functions are required to describe the position of a particle in two dimensions. In three dimensions, 3 functions are required. ( ) x f t = Consider the following two-dimensional vector function: 2cos ,sin 0 2 t t t π = 2 r . The component of r is and the component of is . Hence, we can also describe the vector function by writing x 2cos( ) t y x t r a sin( ) t nd ( ) 2cos ( ) sin . t y t t = = For each t corresponds to a point in the xy plane. You can graph r by plotting these points for by using the parametric plot function on your calculator. The vector is from the origin to a point on the curve. ( ) , t r 0 t ( ) t π -2 -1 1 2 -1 -0.5 0.5 1 r(t) You can see that this vector function traces out an ellipse. If we think of r as representing the position of a particle then ( ) t (1) 2cos(1),sin(1) = (1) r . can also be thought of as a vector. The vector in the plot is r , with its tail starting at the origin.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern