L ESSON 30 – I NTERSECTION OF L INES September 10, 2013 Fernando Morales.
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Transcript of L ESSON 30 – I NTERSECTION OF L INES September 10, 2013 Fernando Morales.
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LESSON 30 – INTERSECTION OF LINESSeptember 10, 2013
Fernando Morales
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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
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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]
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LINEAR SYSTEMS IN 2D (P.463)
Two Distinct LinesUnique pair of numbersExactly one solution or
intersection
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LINEAR SYSTEMS IN 2D (P.463)
Two Coincident Lines0x = 0 or 0y = 0Infinite number of solutions or
intersections
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LINEAR SYSTEMS IN 2D (P.463)
Two distinct but parallel lines0x = 2 or 0y = 1No solutions
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LINEAR SYSTEMS IN 3D (P.465)
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LINEAR SYSTEMS IN 3D (P.465)
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SKEW LINES
• Direction Vectors are non-parallel • No
intersection = No solution
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THE DISTANCE BETWEEN TWO SKEW LINES (P. 468)
• Shortest Distance• Common Perpendicular• Use Projection
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REQUIRED BEFORE NEXT CLASS
Section 8.4 # 1, 2, 4ab, 5ab, 6ab, 8, 10