This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math 23 Sections 110113 B. Dodson Week 3 Homework: 12.5 Lines, Planes 12.6 Quadratic Surfaces 12.7 Cylindrical and Spherical Coords Problem 12.5.3: Give vector and (scalar) parametric equations for the line through the point (2,4,10) parallel to the vector < 3 , 1 , 8 > . Solution: The vector equation OP = OP + td, for when the position vector of the point P ( x, y, z ) puts P on the line through P ( x , y , z ) with direction vector d = < a, b, c > gives < x, y, z > = < x , y , z > + t < a, b, c > = < 2 , 4 , 10 > + t < 3 , 1 , 8 >, which we can view as a “pointslope” equation, where P is the point, and d gives the direction of the line. (Here in the position vector OP, O = O (0 , , 0) is the Origin.) To get the scalar equations, we use scalar mult. and vector add to write the vector equation 2 . as < x, y, z > = < 2 + 3 t, 4 + t, 10 + 8 t >, and simply readoff x = 2 + 3 t, y = 4 + t, z = 10 + 8 t....
View
Full
Document
This note was uploaded on 02/29/2008 for the course MATH 23 taught by Professor Yukich during the Spring '06 term at Lehigh University .
 Spring '06
 YUKICH
 Equations, Scalar, Parametric Equations

Click to edit the document details