(2) (Questions 2 & 3 2) You are going to complete some mathematical analysis to help Angie and Barry, a couple of stressed out math students, who lost a cell phone and tablet while walking in Prospect Park. They need help to figure out how to get their electronics back. The Visitor Center in Prospect Park, denoted O, will be considered the origin of a fixed global coordinate system with (standard basis) vectors el and e2 which point east and north respectively. We are going to assume that Angie and Barry avoided all hills in their walk in the park, and always walked in the plane spanned by eland e2. At 11 AM one morning, Angie was at point A, and Barry was at point B. Their coordinates are given in the table below in terms of the standard basis vectors. The Visitor Center in the park notified the students that their phone and tablet had been located in the park by drone and gave Angie the coordinates of the phone and tablet with respect to the visitor center using el and e2. Angie and Barry do not know Prospect Park and need help navigating Brooklyn to get to their electronics back They each have their own personal bases, Angie's basis is vi and v2 and Barry's is ujand u2. Angie and Barry can only determine locations using coordinates relative to their personal bases Angie and Barry each need to figure out the coordinates of the phone and tablet with respect to their personal bases so that they can figure out which direction to go to get their lost electronics. The data describing the locations is given in the table below and the coordinates are indicated as in the sketch (not to scale) C. Phone Tablet lz (a) Find the transition matrix T that will map the standard basis coordinate vec- tors ei and e to coordinate vectors with respect to Angie's basis v and 2 and use it to answer the following questions. (b) What is the location of the phone in Angie's coordinates? Note: You will need to take into account the fact that the origins of these coordinate systems differ- ent so the displacement from Angie to the phone AC equals the displacement of the Visitor Center to Angie AO, plus the displacement of the phone to the visitors center OC, ie, AC = AO OC (c) What is the location of the tablet in Angie's coordinates? (d) What is the location of the Visitor Center in Angie's coordinates? e) What is the location of Barry in Angie's coordinates? (2) (Questions 2 & 3 2) You are going to complete some mathematical analysis to help Angie and Barry, a couple of stressed out math students, who lost a cell phone and tablet while walking in Prospect Park. They need help to figure out how to get their electronics back. The Visitor Center in Prospect Park, denoted O, will be considered the origin of a fixed global coordinate system with (standard basis) vectors el and e2 which point east and north respectively. We are going to assume that Angie and Barry avoided all hills in their walk in the park, and always walked in the plane spanned by eland e2. At 11 AM one morning, Angie was at point A, and Barry was at point B. Their coordinates are given in the table below in terms of the standard basis vectors. The Visitor Center in the park notified the students that their phone and tablet had been located in the park by drone and gave Angie the coordinates of the phone and tablet with respect to the visitor center using el and e2. Angie and Barry do not know Prospect Park and need help navigating Brooklyn to get to their electronics back They each have their own personal bases, Angie's basis is vi and v2 and Barry's is ujand u2. Angie and Barry can only determine locations using coordinates relative to their personal bases Angie and Barry each need to figure out the coordinates of the phone and tablet with respect to their personal bases so that they can figure out which direction to go to get their lost electronics. The data describing the locations is given in the table below and the coordinates are indicated as in the sketch (not to scale) C. Phone Tablet lz (a) Find the transition matrix T that will map the standard basis coordinate vec- tors ei and e to coordinate vectors with respect to Angie's basis v and 2 and use it to answer the following questions. (b) What is the location of the phone in Angie's coordinates? Note: You will need to take into account the fact that the origins of these coordinate systems differ- ent so the displacement from Angie to the phone AC equals the displacement of the Visitor Center to Angie AO, plus the displacement of the phone to the visitors center OC, ie, AC = AO OC (c) What is the location of the tablet in Angie's coordinates? (d) What is the location of the Visitor Center in Angie's coordinates? e) What is the location of Barry in Angie's coordinates
