Unformatted text preview: line.
x b) A line passes through the points
1
1
3 A( , ‐3) and B( , ).
4
2
2 Determine a direction vector for this line, and write it using integer components. Example 2 Expressing the Equations of Lines Using Vectors Find the parametric and vector equations of a line through A(xo, yo) with direction vector m = (a, b) in R2.
OP = OPo + PoP
l
y
OP = (xo, yo) + tm
r = ro+ tm
(x, y) = (xo, yo) + t(a, b)
x Parametric Equations of Line l:
x = x o + at
y = yo + bt
Vector Equation of Line l:
(x, y) = (xo, yo) + t(a, b)
r = ro + tm
Note: (xo, yo) is any point on the line
m = (a, b) is not unique, ∵any
parallel vector will also work
∴we use tm, with t as the parameter, t εR 2 8.1 Vector and Parametric Equations of a Line in R2.notebook March 08, 2010 Example 3 Reasoning about the vector and parametric equations of a line
Find the vector and parametric equations of a line through:
a) A(‐1, ‐5) and having direction vector m = (3, 2).
b) Sketch the line.
c) Find 2 other points on the line.
y x Example 4 Connecting vector and parametric equations with two points on a line
Find vector and parametric equations of the line through A(3, ‐1) and Q(‐1, 2). 3 8.1 Vector and Parametric Equations of a Line in R2.notebook March 08, 2010 Example 4 Find the vector equation of a perpendicular line.
Consider the line r = (‐4, 3) + t(2, ‐1), t εR
a) Find the direction vector and sketch the line.
b) Find the intercepts.
c) Which point corresponds to the parameter value t = 1?
d) Determine a vector equation for a line that is perpendicular to the given line, and passes through the point P(‐5, 3). y x Homework
page 433 ‐ 434
#1‐6, 8‐12, 14 4...
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This note was uploaded on 04/09/2013 for the course CALCULUS MCV4U taught by Professor N/a during the Spring '13 term at Ccmc School.
 Spring '13
 N/A

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