MCV 4UE Summative Vectors Problem Solving Question Instructions: Your task is to create an original problem solving question with parts (a, b,c,d, etc.) Your question should be a word problem with a real world application of vectors, lines and/or planes. Be creative with the development of your question. Try to include many of the main topics or ideas from the vectors units in your question. Your question should be clearly understandable and make sense in the context of the question. Then, submit your question along with a full solution to the Brightspace dropbox. Example Question: Ms. Pileggi is traveling by plane from Waterloo to London. The distance between the Waterloo airport and the London airport is 112 km. Mr. Law is traveling from Hamilton to Samia by plane. The distance between the Hamilton and Samia airports is 210 km. a) If Ms. Pileggi's plane travels in a straight line from Waterloo to London at a constant speed of 75 km/h at a bearing of 210 degrees, sketch a diagram of the vector that represents her flight. b) If Mr. Law's plane travels in a straight line from Hamilton to Samia at a constant speed of 85 km/h at a bearing of 260 degrees, add Mr. Law's flight to your vector diagram. c) If Ms.Pileggi's flight path can be represented by the line F = (-3.-1.30) +r (1,2. -1) and Mr. Law's flight path by the line 7 = (10. 2, 28) + (7, 1. 1), will their flight paths ever intersect? d) Find the vector, parametric and scalar equations of a plane that is perpendicular to both Ms. Pileggi's and Mr. Law's flights. Main Topics from the vectors units: Geometric Vector Addition Algebraic Vector Addition Magnitude of a Vector The Unit Vector .. . Dot Product Cross Product Properties of Vectors (commutative, associative, distributive, etc.) Vector Applications Equations of lines in 2D and 3D space Scalar, vector, parametric, symmetric forms Equations of planes o Scalar, vector, parametric forms Normal vector Intersections of lines and planes