I need help with this example. Im not sure where to start, if someone could give
ID: 2852130 • Letter: I
Question
I need help with this example. Im not sure where to start, if someone could give me a detailed explanation with step by step solutions, it would be great.
Professor Famsworll's Treasure Hunt As the crew gathers in Planet Express conference room, Professor Fans in Planet Express conference room, Professor Farnsworth steps into the room looking slightly befuddied before realizing where he was. "I have asked you all to come here today for a reason. Instead of wasting your time on poker until our ne:x we are going to have a treasure hunt. The winner will not be determined by luck, but by his or her facility of vector algebra." At this point Amy Wong asks to be excused, stating that the treasure hunt will interfere with her beauty sleep and going out tirme Part 1 ur time on poker until our next assignment, As they all sat around the table the professor fiddled around for a few moments with the remote before the giant TV flickered to life. Turning back to the crew he started to speak, "In front of you is a live feed from where you will begin this adventure. You will see the galactic core (C) at a distance of three parsecs and dead ahead. Five parsecs away and at a distance of four pareecs from C is the planet Nintenduu 64 (N); it appears horizontally to the port (your left) side of C in the live feed. The Planet Express Ship-(E), C, and N are at distance y41, v26. and v10 parsecs respectively from Spa 5 (S), whose Fitness Camp you will all recognize above the horizontal plane. Now I will give you the first hint. Somewhere inside the parallelepiped (PPD) spanned by the three vectors from E to C, N, and S respectively, the treasure lies." As the other members of the crew are busy with these calculations as the team led by Bender Bending Rodriguez flies off to use benders trusty "treasurdar "(Treasure Radar) to "feel the location of the treasure within the space while keeping in touch with Planet Express for further hint Professor Famsworth continues, "form a triangle (T) from the following three points: 1. The centroid of the parallelogram spanned by the vectors EN and ES A point one parsec inward (that is, pointing into the interior of the PPD) along the normal rom the centroid of the parallelogram spanned by the vectors EC and EN A point one parsec inward along the normal line from the centroid of the parallelogram spanned by vectors Eand ES. e treasure is located in the plane of this triangle (T)" A. Find these three points and equation of the plane they form. What is the area of triangle The trea T7 Toranga Leeia decides that with this information and her special pet Nibbler her team can fly Where the diagonat from our ship to the opposite corner of the PPD intersects the plane of After some quick calculations, Philip J Fry's team tlies off to be the first ones on the planet 6. Find the co-ordinates of Crossroads and the distance Fry must ly to get to the planet Is off to tegin their search in this triangle while the {est ol the crew waits for the third h1nt triangle T is the planet 'Crossroads", the treasure is buried somewhere on this planet Crossroads in the interior of T Find the volume of the space that could have contained the treasureExplanation / Answer
There is no time left .
SO, i am giving basic hints.
Take Starting Point as origin.
Imagine all the other point S,C,N
Our goal is to find the Vectors
ES EN EC
Distances are given in the problem ( PARSEC is a unit of distance)
Direction is little bit tricy but you will find them out as soon as you visualize the position of Points.
Use some online Plotting service to visualize better.