06Representation of a Line in the Plane

06Representation of a Line in the Plane - REPRESENTATION OF...

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

View Full Document Right Arrow Icon
R EPRESENTATION OF A L INE IN THE P LANE When describing a line in two dimensions we are used to Cartesian form. This form gives a direct relation between x and y. However, there are other different ways of describing a line in two or three dimensions. Cartesian form (in 2D) – coordinates of a point on the line and the slope of the line Vector form – position vector of a point on the line and a vector parallel to the line (note: this is also sometimes called parametric form) Consider a line which passes through point A and is parallel to vector b . b R A To find the vector equation of this line, r , consider a general point R on the line. Let R have position vector r. R A is parallel to b , therefore b t R A = , but r a R A + - = . Therefore, b t r a = + - and b t a r + = . The vector form of a line is d t p r + = , where p is any point on the line, d is any vector in the direction of the line, and t is any value. The parametric form is +
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 07/12/2011 for the course MATH 241 taught by Professor Kim during the Fall '08 term at University of Illinois, Urbana Champaign.

Page1 / 3

06Representation of a Line in the Plane - REPRESENTATION OF...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online