#### Assignment 1: Writing a simple class and testing it

Goals: Practice designing the representation of data, writing getter methods and testing them.

##### 1` `Instructions

This homework should be done individually.

the names of classes,

the names and types of the fields within classes,

the names, types and order of the arguments to the constructor, or

filenames

Due Date: Check the deadline on the handins server.

##### 2` `Vectors

##### 2.1` `Introduction

Vectors are commonly used in Math and physics. A vector (in 3D) is signified by a direction and a length (magnitude). It is commonly represented as three components: x, y and z. Some operations on vectors include:

Magnitude: for a vector \(v\) this is denoted as \(|v|\)=\(\sqrt{x^2+y^2+z^2}.\)

Normalizing a vector: this is a vector that is obtained by dividing each component of a vector by its magnitude.

Addition of two vectors: a vector sum is a vector that is obtained by adding respective components of the two vectors.

Multiplying a vector by a constant: this produces a vector obtained by multiplying each component of the current vector by the provided constant.

Dot product: The dot product of two vectors v=\((v_x,v_y,v_z)\) and w=\((w_x,w_y,w_z)\) is defined as a number \(v \cdot w = v_x*w_x + v_y*w_y + v_z*w_z\).

Angle between two vectors: This is defined as \(cos(\theta) = \frac{v \cdot w}{|v||w|}\). Technically given two vectors, there are two angles between them. This returns the shorter of the two angles. For example, if the two vectors align with the clock hands at 3pm, this would return 90 degrees.

##### 2.2` `What to do

A constructor that takes in x, y, z components of the vector.

Methods to get the values of individual components (e.g. getX ,etc.).

A toString method that returns a string that describes this vector. This string should be of the form “(x,y,z)” replacing the letters with their values. Each component should be formatted to round to exactly two decimal places (look at the String.format method to see how to do this).

A method getMagnitude that returns its magnitude.

A method normalize that returns a normalized version of this vector.It should throw an IllegalStateException object if this operation cannot be completed.

A method add that returns the result of adding this vector to another vector. It should not change the vectors that are being added.

A method multiply that returns the result of multiplying this vector by a constant. It should not change the vector that is being multiplied.

A method dotProduct that returns the dot product of this vector and another vector. It should not change the two vectors.

A method angleBetween that returns the angle between two vectors in degrees. It should not change the two vectors. It should throw an IllegalStateException if this operation cannot be completed.

Design the signature of the method.

Write Javadoc-style comments for that method.

Write the body for the method.

Write one or more tests that check that the method works as specified in all cases.

You may find the Math class useful for this assignment. Look at the documentation for the Math class and try to understand how to use it.

##### How to submit

Create a zip file that contains directly your src and test folders. When you unzip the file, you should see only these two folders.

Log on to the Bottlenose submission server.

Navigate to Assignment 1 and submit the zip file.

Wait for a few minutes for feedback to appear, and take action if needed.