9/2/2015
1
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MATM1544
LECTURE 21
The vector equation
of a line
September 2, 2015
T: 051 401 9111
[email protected]
CONTENT
•
Vector equation of a line
•
Parametric equations of a line
•
Examples
•
Exercise
9/2/2015
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RECAP THE VECTOR EQUATION OF A LINE
° = °
±
+ ²³
³
:
Vector on or parallel to the line.
°
±
:
Any point on the line with position vector
°
±
.
°:
General point
(x, y, z)
on line with position vector
°
.
²:
Parameter where
−∞ < ´ < ∞
Then
°
= °
±
+ ²³
.
PARAMETRIC EQUATIONS OF A LINE
If the point on the line has a position vector b
°
= µ
+ ²³
We get
°
=
¶
·
¸
=
µ
¹
µ
º
µ
»
+ ²
³
¹
³
º
³
»
=
µ
¹
+ ²³
¹
µ
º
+ ²³
º
µ
»
+ ²³
»
or
¶ = µ
¹
+ ²³
¹
· = µ
º
+ ²³
º
¸ = µ
»
+ ²³
»
Parametric equations of the line.
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EXAMPLE
Example 1.
The point
(1,2,1)
is on a certain line, which is
parallel to the vector
(1, −3, 1)
.
(a)
Find the vector equation of the line.
(b) Find the parametric equations of the line.
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 Summer '20
 Parametric equation, vector equation of a line