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Chapter 9.5

MATH 2400 Chapter Notes - Chapter 9.5: Linear Equation, Line Segment

Course Code
MATH 2400
Markus Steindl

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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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