Sec10.5 - Sec. 10.5 Equation of Lines and Planes In 2D a...

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

View Full Document Right Arrow Icon
Sec. 10.5 Equation of Lines and Planes In 2D a line is determined by a point and a slope (direction). In 3D a line L is determined by a point 00 0 0 (, ,) Px y z = and the direction of L which is given by a vector v that is parallel to L . The vector equation of line L: 0 rrt v =+ (Putting bounds on t will yield a line segment.) As t varies the line is traced out by the tip of vector r. (v is the directional vector of the line.) Let v = < a, b, c > Æ tv = < at, bt, ct >. Let r = < x, y, z > and 0 0 ,, rx y z = <> . Substituting into the vector equation of the line we can get the component form. The component form of the vector equation of line L: 000 a t y b t z c t = <+ + +> Since two vectors are equal if and only if their components are equal, we get the parametric form of a line in 3 space where t is a real number. The parametric form of line L: 0 0 0 x xa t y yb t zz c t through 0 0 y z = and parallel to v = < a, b, c >. Note: The vector form and the parametric form are not unique!
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 01/28/2010 for the course MATH 2224 taught by Professor Mecothren during the Spring '03 term at Virginia Tech.

Page1 / 4

Sec10.5 - Sec. 10.5 Equation of Lines and Planes In 2D a...

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