Find if point lays on line segment

Question

I have line segment defined by two points A(x1,y1,z1) and B(x2,y2,z2) and point p(x,y,z). How can I check if the point lays on the line segment?

Answer 1

I use this to calculate the distance AB between points a and b.

static void Main(string[] args)
{
        double AB = segment(0, 1, 0, 4);
        Console.WriteLine("Length of segment AB: {0}",AB);
}

static double segment (int ax,int ay, int bx, int by)
{
    Vector a = new Vector(ax,ay);
    Vector b = new Vector(bx,by);
    Vector c = (a & b);
    return Math.Sqrt(c.X + c.Y);
}

struct Vector
{
    public readonly float X;
    public readonly float Y;

    public Vector(float x, float y)
    {
        this.X = x;
        this.Y = y;
    }
    public static Vector operator &(Vector a, Vector b)  
    {
        return new Vector((b.X - a.X) * (b.X - a.X), (b.Y - a.Y) * (b.Y - a.Y));
    }
}

based on Calculate a point along the line A-B at a given distance from A