How to create and apply rotation matrix to vector

Question

I'am creating my first ray tracing program in C and I'am currently trying to rotate the camera. Basically , change the direction of the ray origin.

I already have a ray direction, which is a vector and I want to apply a rotation matrix to this Vector.

void    render(void)
{
    t_Color     color;
    int         x;
    int         y;
    t_Vector    d;

    x = ((canvas()->width / 2) * -1);
    y = (canvas()->height / 2);
    while (--y >= (canvas()->height / 2) * -1)
    {
        while (++x <= (canvas()->width / 2))
        {
            d = canvas_to_viewport(x, y);
            color = trace_ray(d, 1, INT_MAX);
            put_pixel(x, y, color);
        }
        x = ((canvas()->width / 2) * -1);
    }
}

What I want to do is basically, change this line :

// d represents the ray direction

d = canvas_to_viewport(x, y);

to

// d represents the ray direction after rotating

d = rotation_matrix * canvas_to_viewport(x, y);

My program will receive some input in the form of :

3d normalized orientation vector. In range [-1,1] for each x,y,z axis:
0.0,  0.0,  1.0

Those coordinates should indicate the orientation for my camera. I must admit linear algebra is not my strongest point, so I would like to know how can I convert those orientation coordinates into a rotation matrix and how to multiply it by a vector to get another vector , hopefully, indicating the new direction.