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Chapter 9.5

Department

MathematicsCourse Code

MATH 2400Professor

Markus SteindlChapter

9.5This

**preview**shows half of the first page. to view the full**2 pages of the document.**Anna Pyle

University of Colorado Fall 2016

MATH2400 Calculus 3

Textbook: CALCULUS concepts & contexts 4 James Stewart

9.6: Equations of Lines and Planes

oA line L in three-dimensional space is determined by a point and a direction

oA vector equation is given below where each value of the parameter t gives the position vector

r of a point on L

oTwo vectors are equal if and only if corresponding components are equal

oThe equations shown below are called parametric equations of the line L through the point Po

and parallel to the vector v=<a,b,c>. Each value of the parameter t gives a point (x,y,z) on L

oIf a vector v = <a,b,c> is used to describe the direction of a line L, then the numbers a,b, and c

are called direction numbers of L

oAnother way of describing a line is to solve each of the equations above for t, and obtain

symmetric equations, which are shown below:

oLine segment equations are shown below:

oSkew Lines

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