do i use linear combination for this problem ??? You are a young adventurer. Having spent most of your time in the mythical city of Oronto, you decide toleave home for the first time. Your parents want to help you on your journey, so just before your departure,they give you two gifts. Specifically, they give you two forms of transportation: a hover board and a magiccarpet. Your parents inform you that both the hover board and the magic carpet have restrictions in howthey operate:[³]. By thisWe denote the restriction on the hover board's movement by the vectorwe mean that if the hover board traveled "forward" for one hour, it would move alonga "diagonal" path that would result in a displacement of 3 km East and 1 km Northof its starting location.We denote the restriction on the magic carpet's movement by the vector [2]. By thiswe mean that if the magic carpet traveled “forward" for one hour, it would movealong a "diagonal" path that would result in a displacement of 1 km East and 2 kmNorth of its starting location.Scenario Two: Hide-and-SeekOld Man Gauss wants to move to a cabin in a different location. You are not sure whether Gauss is justtrying to test your wits at finding him or if he actually wants to hide somewhere that you can't visit him.Are there some locations that he can hide and you cannot reach him with these two modes oftransportation?Describe the places that you can reach using a combination of the hover board and the magic carpet andthose you cannot. Specify these geometrically and algebraically. Include a symbolic representation usingvector notation. Also, include a convincing argument supporting your answer.

Answered: You are a young adventurer. Having…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

do i use linear combination for this problem ???

You are a young adventurer. Having spent most of your time in the mythical city of Oronto, you decide to
leave home for the first time. Your parents want to help you on your journey, so just before your departure,
they give you two gifts. Specifically, they give you two forms of transportation: a hover board and a magic
carpet. Your parents inform you that both the hover board and the magic carpet have restrictions in how
they operate:
[³]. By this
We denote the restriction on the hover board's movement by the vector
we mean that if the hover board traveled "forward" for one hour, it would move along
a "diagonal" path that would result in a displacement of 3 km East and 1 km North
of its starting location.
We denote the restriction on the magic carpet's movement by the vector [2]. By this
we mean that if the magic carpet traveled “forward" for one hour, it would move
along a "diagonal" path that would result in a displacement of 1 km East and 2 km
North of its starting location.
Scenario Two: Hide-and-Seek
Old Man Gauss wants to move to a cabin in a different location. You are not sure whether Gauss is just
trying to test your wits at finding him or if he actually wants to hide somewhere that you can't visit him.
Are there some locations that he can hide and you cannot reach him with these two modes of
transportation?
Describe the places that you can reach using a combination of the hover board and the magic carpet and
those you cannot. Specify these geometrically and algebraically. Include a symbolic representation using
vector notation. Also, include a convincing argument supporting your answer.

Expert Solution

Step 1

Here, in the question, we are given a situation of a young traveler like me who had spent most of his time in the mythical city of Toronto. I decided to leave home for the first time. My parents want to help me on my journey. Two forms of transportation are given: Magic board and a hoverboard. Parents tell me that their are restrictions on their operation.

We have to describe the locations that he can hide and cannot reach with these two modes of transportation.

A combination of the hoverboard and the magic carpet is to be used. We have to specify the situation geometrically and algebraically.