1. 7.4 - The Intersection of 2 Lines
MCV4U1
7.4 - The Intersection of 2 Lines
Possible Cases:
1.) No Intersection
- The lines are Parallel
and distinct.
2.) Infinite Solutions
- The lines are coincident.
3.) Unique Solution
- The lines intersect at
a point.
4.) No Intersection
- The Lines are SKEW
- The lines are neither parallel nor intersecting. They lie in parallel planes.

2. Intersection Flowchart:
START
2 Equations of Lines
Check if Direction Vectors
Are Scalar Multiples
YES NO
Check If Point From
one line is on the other
line.
Infinite Solutions
COINCIDENT
LINES
NO Solution
Parallel And Distinct
Lines
Equate Parametric Equations of Both lines, and SOLVE for both parameters. (Check in 3rd PE)
Unique Solution
Lines Intersect at a
Point
No Solution
Skew Lines

3. interpretation of each.
Ex.) Find the intersection of each of the following pairs of lines. Provide a geometric
interpretation of each.
a) r = (1, 2, 3) + t(1, -1, 1) and r = (2, 3, 5) + s(-3, 3, -3)
b) r = (2, 3) + t(-3, 5) and r = (1, 4) + s(3, -2)
c) x = t and x = t
y = 2 + 2t y = -6 -5s
z = t z = -3 - s
d) r = (-2, 1, 0) + t(1, 3, 7) and

4. Homework: p. 263 # 3 - 8, 11, 13

5. Attachments