U Vectors - Geomet X U Vectors - Geomet X U Vectors - Geomet X Vectors - Geomet X Sy 13,-3, 61 X Sy Vector Dot Produ X Online calculator. X Homework Help X + V X - -> C a eclass.yorku.ca/mod/quiz/review.php?attempt=4598476&cmid=2203074 L Question 4 Round your answers to two digits after the decimal. Partially correct Q- Mark 0.30 out of In this question, we are considering the geometry of planes - which also have several equivalent representations. 3.00 Visualizing what's going on with planes is a bit more challenging. It's worth trying though! As before - take your time! Flag question Winter To start, you may recall that any three points that do not lie on a line define a 2-dim'l plane. For example, the three points A = (10, 6, 35), B = (6, 18, -9), and C = (14, 12, 43) define a (unique) plane P. 14 P : 18 + ( 1 - s -t ) . 12 43 This equation can generate the coordinates for all of the above three points. For example, if we set t = 0 X and s = x we recover the point A. Support Part a. First, express the plane P in coordinate representation. That is, write the third coordinate as a linear function of the first two coordinates o Logic x3 = a . x1 + b . x2 + c where II: . the slope in direction of the first axis a = -4 X s (due . the slope in direction of the second axis b = 5 X . the intercept c = 2 apters 11 4) This characterization of a plane is unique. Any combination of a slope and an intercept determines a unique plane! Sunny Q Search ENG 10:39 PM US 2023-03-26 10U Vectors - Geomet X U Vectors - Geomet X U Vectors - Geomet X Vectors - Geomet X Sy 13,-3, 61 X Sy Vector Dot Produ X Online calculator. X Homework Help X + V X + -> C a eclass.yorku.ca/mod/quiz/review.php?attempt=4598476&cmid=2203074 L Part b. Next, any three different points that lie on a plane and not on a line form a characterization of a plane by three N1540 Q points. This characterization is not unique. Many point triplets can define the same plane! ctory We need to figure out whether points lie on the plane or not. Which (if any) of the following points lie on plane P? atical ics II (Winter . The point with the coordinates (14, 8, 51) does not * x lie on the plane P. 023) . The point with the coordinates (17, 11, 62) does not * ~ lie on the plane P. ants . The point with the coordinates (7, 18, -4) does * lie on the plane P. tencies Part c. A plane can also be represented using an on-point and two directions. For example, we can represent the plane P using A as the onpoint: 10 W1 P : + U2 U3 W3 es and such that we obtain strative Support . point A ift = s = 0 . point Bift = 1, s = 0 odule 1: . point Cift = 0, s = 1 ction to Logic 3rd) In that case, we must have . ug = 6 X odule II: ction to . UQ = 10 X atorics (due rd) . 73 10 . W1 5 X 1: Chapters 11 eek 1-4) 702 X 2: Chapters 13 . W3 3 X 8.C 2023-03-26 10 Sunny Q Search ENG 10:40 PM USU Vectors - Geomet X U Vectors - Geomet X U Vectors - Geomet X Vectors - Geomet X Sy 13,-3, 61 X Sy Vector Dot Produ X M Online calculator. X Homework Help X + V X - > C a eclass.yorku.ca/mod/quiz/review.php?attempt=4598476&cmid=2203074 E eClass English (en) 2 Ask SAVY Lina Tran The same plane can be represented using different on-points and directions. Indeed, any point on the plane along with AP/ECON1540 Q - two direction vectors that lie in the plane will do. Can you come up with another such representation for the above Introductory plane? Mathematical Part d. Finally, consider the on-point and orthogonality representation. Here we are expressing the plane as a collection Economics II (Winter of points such that the difference with an on-point vector is orthogonal (dot product = 0!) to a given vector. For 2022-2023) example, we can express the plane P as the collection of all vectors x that satisfy Participants P: (01 02 -1) . Competencies where Grades 01 -4 O General 5 X Resources and 2 = 5 Administrative Support Mini-Module I: To convince yourself that this equation describes the plane , check that the coordinates of all three points satisfy this Introduction to Logic equation! For more details on this representation see figure 15.9.3 and equation 15.9.5 in the textbook on p. 619. (due Feb 3rd) As other representations, this one is not unique. To convince yourself find the parameters in the following representation such that the equation characterizes the plane P. Mini-Module II: 14 Introduction to P : (01 02 4) 2 2 12 Combinatorics (due X 3 March 3rd) You find: Module 1: Chapters 11 & 12 (week 1-4) 01 = -5 . 09 = 2 Module 2: Chapters 13 & 14 (week 5-7) 3 X 8.C ENG 10:41 PM US 2023-03-26 10 Sunny Q Search