旋转矩阵没有正确应用于向量

我正在尝试在 OpenGL 中学习转换，我正在使用 glm 进行数学计算。我有一个向量&我想对该向量应用一些旋转。但是我得到的输出为vec3(0,0,0)

#define GLM_ENABLE_EXPERIMENTAL
#include <glm/ext/matrix_float4x4.hpp> // mat4x4
#include <glm/ext/matrix_transform.hpp> // translate, rotate, scale, identity
#include <glm/gtx/string_cast.hpp>
#include<iostream>
int main(){
        //define  a 4x4 model matrix
        glm::mat4 model;
        //define a vector
        glm::vec4 Position = glm::vec4(glm::vec3(0.4,0.2,0.2), 1.0);
        //create a model matrix with rotation of 45 degrees around z aixs
        model = glm::rotate(model,  45.0f, glm::vec3(0.0f, 0.0f, 1.0f));        
        //print the final vector position after rotation is applied
        std::cout<< glm::to_string(model*Position) <<std::endl;
        return 0;
}