$*$use java$*$Imagine yourself as an astronaut $($represented as $3$D vector$)$ on a space

mission to explore a distant galaxy. As you navigate through space, you will

encounter various celestial bodies represented as $3$D vectors. Your mission is

to perform vector operations to reach your destination. Let me to guide you

on how to solve the problem:

In the class Vector$3$D$,$ define the components of the vector $($i$.$e$.,$ x$,$y$,$

z $).$ It is necessary to encapsulate your data since a client program,

SpaceMission, will use this class later.

Implement the methods provided in the UML diagram below for the

Vector$3$D class. These methods cover the fundamental vector

operations.

Now you should implement the SpaceMission class from scratch based

on the provided UML diagram.

The instance variable of this class shows your position in the space.

Now, you have identified an interesting celestial body that you wish to

travel to$.$ To assess its feasibility, follow the steps below:

i$.$ First, measure the distance between your current position

and the location of the celestial body, which is represented

by another vector. For this, Implement

distanceTo $($Vector$3$D$)$ method.

ii$.$ To facilitate travel, there are instances where you need to

refuel by certain amounts. This process involves vector

scalar multiplication. When a vector is multiplied by a

scalar, the length $($magnitude$)$ of the vector increases

proportionally to the scalar factor. To achieve this,

implement the method refuel $($double$)$ in which you must

use scalarMultiplication as defined in the Vector$3$D

class.

iii. Now, use the two methods mentioned above to implement

navigate $($Vector$3$D$,$ double, double$).$ This function

checks the distance to the specified celestial body. If the

distance is more than or equal to the provided threshold,

you reposition yourself to where the celestial body is$.$ If

not, you repeatedly refuel yourself by the given refuel

amount until the distance is more than or equal to the

provided threshold. At this point, you reposition yourself.

Please note that, as the JavaDoc explains, the first input

parameter represents the position of the celestial body,

the second is the threshold, and the third is the amount by

which you refuel yourself.

Please note that, as usual, the signature of the method should not change if

it is given. If it is not provided, then the signature should match what is

given in the JUnit test cases.