MCV4U1-UNIT EIGHT-LESSON ONE
Lesson One: Vector, Parametric, and Symmetric Equations of a Line in  2
P
L
P1
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d  a, b 
Let L be a line in  2 .
Let Px, y  represent any point on L.
Let Px1 , y1  represent a specific point on L.
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Let d  a, b  be parallel to L. (called the direction vector)
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
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Using triangle law of addition of vectors, the vector equation of L is.... OP  OP1  P1 P
In component form, x, y   x1 , y1   t a, b
The parametric equations are.....
x  x1  ta
y  y1  tb
x  x1  ta
or
y  y1  tb
The symmetric equations are.....
x  x1 y  y1

a
b
Note: If you cross multiply , you end up with the familiar standard form of a
line Ax+By+C=0
Example 1:
Find the vector equation of the line through (1,3) and (5,2).
Example 2:
Find the parametric equations of the line with y-intercept 3, and parallel to the line x+2y-8=0
Example 3:
Find the symmetric equations of the line parallel to the x-axis and passing through the point (7,-2).