Download lines intersect - Quantum Tunneling

LESSON 30 – INTERSECTION OF
LINES
September 10, 2013
Fernando Morales
LEARNING GOALS
Recognize
geometrically
intersection of lines in
two-space and threespace
 Solve for the point of
intersection of lines in
various different ways
 Derive the formula for
measuring the
shortest distance
between skew lines

PEER INSTRUCTION
Given a system of linear equations in two-space,
how many types of solutions are possible?
Explain.
[K, C]
 The direction vectors of two lines in three-space
are not parallel. Does this indicate that the
lines intersect? Explain.
[A, C]
 How can you tell if two lines are in three-space
are skew? Use examples to explain.
[A, C]

LINEAR SYSTEMS IN 2D (P.463)
 Two
Distinct Lines
 Unique pair of numbers
 Exactly one solution or intersection
LINEAR SYSTEMS IN 2D (P.463)
 Two
Coincident Lines
 0x = 0 or 0y = 0
 Infinite number of solutions or
intersections
LINEAR SYSTEMS IN 2D (P.463)
 Two
distinct but parallel lines
 0x = 2 or 0y = 1
 No solutions
LINEAR SYSTEMS IN 3D (P.465)
LINEAR SYSTEMS IN 3D (P.465)
SKEW LINES
• Direction Vectors
are non-parallel
• No intersection
= No solution
THE DISTANCE BETWEEN TWO SKEW LINES
(P. 468)
• Shortest Distance
• Common Perpendicular
• Use Projection
REQUIRED BEFORE NEXT CLASS

Section 8.4 # 1, 2, 4ab, 5ab, 6ab, 8, 10