Lesson 30 – Intersection of Lines

LESSON 30 – INTERSECTION OF LINESSeptember 10, 2013Fernando Morales

LEARNING GOALS Recognize

geometrically intersection of lines in two-space and three-space

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 LinesUnique pair of numbersExactly one solution or

intersection

LINEAR SYSTEMS IN 2D (P.463)

Two Coincident Lines0x = 0 or 0y = 0Infinite number of solutions or

intersections

LINEAR SYSTEMS IN 2D (P.463)

Two distinct but parallel lines0x = 2 or 0y = 1No 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