# include <stdio.h>
# include <math.h>

int main ( )
{
  float pi = 3.14159265;
  float u[2];
  float u_cross_v;
  float u_dot_v;
  float u_norm;
  float uv_angle;
  float uv_cosine;
  float v[2];
  float v_norm;
  float x;
  float y;

  printf ( "Enter x, y for vector 1: " );
  scanf ( "%f%f", &x, &y );
  u[0] = x;
  u[1] = y;

  printf ( "Enter x, y for vector 2: " );
  scanf ( "%f%f", &x, &y );
  v[0] = x;
  v[1] = y;
//
//  Compute the norms of the two vectors.
//
  u_norm = sqrt ( u[0] * u[0] + u[1] * u[1] );

  printf ( " ||u|| = %g\n", u_norm );

  v_norm = sqrt ( pow ( v[0], 2 ) + pow ( v[1], 2 ) );

  printf ( " ||v|| = %g\n", v_norm );
//
//  The dot product of two vectors is 0 if they are perpendicular to each other.
//
  u_dot_v = u[0] * v[0] + u[1] * v[1];
  printf ( " u.v = %g\n", u_dot_v );

  u_cross_v = u[0] * v[1] - u[1] * v[0];
  printf ( " uxv = %g\n", u_cross_v );
//
//  The cosine of the angle between two vectors is the dot product divided by their norms.
//
  uv_cosine = u_dot_v / u_norm / v_norm;
  printf ( " cosine(u,v) = %g\n", uv_cosine );
//
//  The ANGLE between two vectors is the inverse cosine or "arc-cosine" of the cosine.
//  This will come out in RADIANS unless we divide the result by PI and multiply by 180.
//
  printf ( "\n" );
  uv_angle = acos ( uv_cosine );
  printf ( " angle(u,v) = %g radians\n", uv_angle );
  uv_angle = uv_angle / pi * 180;
  printf ( " angle(u,v) = %g degrees\n", uv_angle );

  return 0;
}