diff --git a/.gitignore b/.gitignore
index 226ada1..2b70b8a 100644
--- a/.gitignore
+++ b/.gitignore
@@ -100,3 +100,11 @@ CTestTestfile.cmake
 _deps
 CMakeUserPresets.json
 
+# Build / Compiled program
+
+build/Render
+build/bin/*
+Render
+build/Render.exe
+Render.exe
+
diff --git a/ROADMAP.md b/ROADMAP.md
index c2f166a..b49e491 100644
--- a/ROADMAP.md
+++ b/ROADMAP.md
@@ -5,13 +5,17 @@ This roadmap breaks down the essential steps to build your CPU-based raytracer f
 ---
 
 ## Phase 1: Foundations & Core Engine
-- [ ] Set up vector math utilities (`vec3`): add, subtract, dot, cross, normalize  
+- [x] Set up vector math utilities (`vec3`): add, subtract, dot, cross, normalize  
 - [ ] Implement Ray class — origin, direction, basic functions  
 - [ ] Basic Sphere object — position, radius, material properties  
 - [ ] Ray-Sphere intersection logic — the core of your renderer  
 - [ ] Camera setup — generate rays through the viewport  
 - [ ] Scene structure — manage objects and lights  
 
+# Objectives:
+  - [ ] Render a single sphere with basic color
+  - [ ] Output to a simple PPM file format
+
 ---
 
 ## Phase 2: Lighting & Shading Basics
diff --git a/build/bin/test b/build/bin/test
deleted file mode 100755
index e9a1248..0000000
Binary files a/build/bin/test and /dev/null differ
diff --git a/include/vector/utils_vec.cpp b/include/vector/utils_vec.cpp
new file mode 100644
index 0000000..79bfcfc
--- /dev/null
+++ b/include/vector/utils_vec.cpp
@@ -0,0 +1,49 @@
+#include "utils_vec.hpp"
+
+vec3 vec3::operator+(const vec3 &other) const
+{
+    return vec3(x + other.x, y + other.y, z + other.z);
+}
+
+vec3 vec3::operator-(const vec3 &other) const
+{
+    return vec3(x - other.x, y - other.y, z - other.z);
+}
+
+vec3 vec3::operator*(float scalar) const
+{
+    return vec3(x * scalar, y * scalar, z * scalar);
+}
+
+vec3 vec3::operator/(float scalar) const
+{
+    if (scalar == 0)
+    {
+        fprintf(stderr, "Error: Division by zero in vec3::operator/.\n");
+    }
+    return vec3(x / scalar, y / scalar, z / scalar);
+}
+
+vec3 vec3::dot(const vec3 &other) const
+{
+    return vec3(x * other.x, y * other.y, z * other.z);
+}
+
+vec3 vec3::cross(const vec3 &other) const
+{
+    return vec3(
+        y * other.z - z * other.y,
+        z * other.x - x * other.z,
+        x * other.y - y * other.x);
+}
+
+vec3 vec3::normalize() const
+{
+    float length = sqrt(x * x + y * y + z * z);
+    if (length == 0)
+    {
+        fprintf(stderr, "Error: Normalization of zero vector in vec3::normalize.\n");
+        return vec3(0, 0, 0); // Return zero vector if normalization fails
+    }
+    return vec3(x / length, y / length, z / length);
+}
\ No newline at end of file
diff --git a/include/vector/utils_vec.hpp b/include/vector/utils_vec.hpp
new file mode 100644
index 0000000..ee56b19
--- /dev/null
+++ b/include/vector/utils_vec.hpp
@@ -0,0 +1,37 @@
+#ifndef UTILS_VEC_HPP
+#define UTILS_VEC_HPP
+
+#include <cstddef>
+#include <cstdlib>
+#include <stdio.h>
+#include <stdlib.h>
+#include <cmath>
+
+class vec3
+{
+private:
+    float x, y, z;
+
+public:
+    vec3() : x(0), y(0), z(0) {}
+    vec3(float x, float y, float z) : x(x), y(y), z(z) {}
+
+    float getX() const { return x; }
+    float getY() const { return y; }
+    float getZ() const { return z; }
+
+    void setX(float val) { this->x = val; }
+    void setY(float val) { this->y = val; }
+    void setZ(float val) { this->z = val; }
+
+    vec3 operator+(const vec3 &other) const;
+    vec3 operator-(const vec3 &other) const;
+    vec3 operator*(float scalar) const;
+    vec3 operator/(float scalar) const;
+
+    vec3 dot(const vec3 &other) const;
+    vec3 cross(const vec3 &other) const;
+    vec3 normalize() const;
+};
+
+#endif // !UTILS_VEC_HPP
diff --git a/source/main.cpp b/source/main.cpp
index df28b27..3874686 100644
--- a/source/main.cpp
+++ b/source/main.cpp
@@ -1,7 +1,29 @@
 #include <iostream>
 
+// Include the vector utilities header file
+#include "vector/utils_vec.hpp"
+
 int main()
 {
-    std::cout << "Hello, World!" << std::endl;
+    vec3 *v1 = (vec3 *)malloc(sizeof(vec3) * 2);
+
+    if (v1 == nullptr)
+    {
+        fprintf(stderr, "Error: Memory allocation failed for vec3 array.\n");
+        return 1; // Exit with error code
+    }
+
+    for (int i = 0; i < 2; i++)
+    {
+        v1[i].setX(i + 1.0f);
+        v1[i].setY(i + 2.0f);
+        v1[i].setZ(i + 3.0f);
+    }
+
+    vec3 v2 = v1[0] + v1[1];
+
+    std::cout << "v2: (" << v2.getX() << ", " << v2.getY() << ", " << v2.getZ() << ")" << std::endl;
+
+    free(v1); // Free the allocated memory
     return 0;
 }
\ No newline at end of file