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

float vector_angle ( int n, float x[], float y[] );
float vector_dot ( int n, float x[], float y[] );
float vector_norm ( int n, float x[] );


int main ( void )
{
  float degrees;
  int i;
  int n;
  float pi = 3.14159265;
  float radians;
  float x_dot_y;
  float x_norm;
  float y_norm;

  printf ( "Enter vector dimension n: " );
  scanf ( "%i", &n );
//
//  We have to wait til we now the value of N in order to declare
//  the vectors X and Y as "VLA's":
//
  float x[n];
  float y[n];
//
//  We have to read in the entries one at a time.
//
  printf ( "Enter the %i values of vector X: ", n );
  for ( i = 0; i < n; i++ )
  {
    scanf ( "%f", &x[i] );
  }

  printf ( "Enter the %i values of vector Y: ", n );
  for ( i = 0; i < n; i++ )
  {
    scanf ( "%f", &y[i] );
  }

  x_norm = vector_norm ( n, x );
  y_norm = vector_norm ( n, y );

  printf ( "  X norm is %g\n", x_norm );
  printf ( "  Y norm is %g\n", y_norm );

  x_dot_y = vector_dot ( n, x, y );

  printf ( "  X dot Y is %g\n", x_dot_y );

  radians = vector_angle ( n, x, y );
  degrees = radians * 180.0 / pi;

  printf ( "  Angle is %g radians, %g degrees\n", radians, degrees );

  return 0;
}

float vector_angle ( int n, float x[], float y[] )
{
  float c;
  int i;
  float value;

  c = vector_dot ( n, x, y ) / vector_norm ( n, x ) / vector_norm ( n, y );
  value = acos ( c );

  return value;
}
float vector_dot ( int n, float x[], float y[] )
{
  int i;
  float value;

  value = 0.0;
  for ( i = 0; i < n; i++ )
  {
    value = value + x[i] * y[i];
  }

  return value;
}

float vector_norm ( int n, float x[] )
{
  int i;
  float value;

  value = 0.0;
  for ( i = 0; i < n; i++ )
  {
    value = value + x[i] * x[i];
  }
  value = sqrt ( value );

  return value;
}