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.

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

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 = -5 + 3t and x = t y = 2 + 2t y = -6 -5s z = -7 + 6t z = -3 - s d) r = (-2, 1, 0) + t(1, 3, 7) and

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

Attachments