An orthogonal vector is defined by two real values a, b and written in the form ai+bj. We define equality for two vectors v1=ai+bj and v2=ci+dj as follows:

(v1 == v2) if and only if (a = c) and (b = d)

Given is a class Vector that encapsulates an orthogonal vector. Your task is to write an immutable version of this class and implement the following methods: toString that returns a string representation of the vector; equals that returns true if this equals that, false otherwise; compareTo that implements the Comparable interface and hashCode. The comparison, for compareTo, is based on a comparison of the coefficients of i, and if equal, on the coefficients of j.

class Vector implements Comparable{

private double a,b;

Vector(double a0, double b0){

a = a0; b = b0;

}

}

Write a separate class and test code.

Be sure to test the code to make sure it works correctly.