//      Vec3D.java

//      This class defines a three-dimensional vector.

class Vec3D {
	public double x,y,z;			     // Vec3D components
	
	public Vec3D() { x=y=z=0; }		   // constructors
	public Vec3D(double pX, double pY)
	{	x=pX;	y=pY;	z=0;	}
	public Vec3D(double pX, double pY, double pZ)
	{	x=pX;	y=pY;	z=pZ;	}

	// settors
	
	public void Set(double pX, double pY)
	{	x=pX;	y=pY;	z=0;	}
	public void Set(double pX, double pY, double pZ)
	{	x=pX;	y=pY;	z=pZ;	}

	// Vec3D arithmatic

	public Vec3D Plus(Vec3D pV) 
	{ return new Vec3D( x+pV.x, y+pV.y, z+pV.z ); }

	public void Add(Vec3D pV) 
	{ x = x+pV.x; y = y+pV.y; z = z+pV.z; }

	public Vec3D Minus(Vec3D pV) 
	{ return new Vec3D( x-pV.x, y-pV.y, z-pV.z );  }

	public void Subtract(Vec3D pV) 
	{ x = x-pV.x; y = y-pV.y; z = z-pV.z; }

	public double Dot(Vec3D pV)		 // dot product
	{ return x*pV.x + y*pV.y + z*pV.z; }

	public Vec3D Cross(Vec3D pV)	 // cross product
	{ return new Vec3D( y*pV.z-z*pV.y, z*pV.x-x*pV.z, x*pV.y-y*pV.x );  }

	public Vec3D Times(double pR)	   // * a scalar
	{ return new Vec3D( x*pR, y*pR, z*pR );  }

	public Vec3D DividedBy(double pR)	   // divide by a scalar
	{ return new Vec3D( x/pR, y/pR, z/pR );  }

	// magnitude

	public double LenSqr()
	{ return x*x+y*y+z*z; }

	public double Length()
	{ return Math.sqrt(LenSqr()); }

	// projection (component of this parallel to pV)
	// Note: component perpendicular to pV is:  *this - Proj(pV)

	public Vec3D Proj(Vec3D pV)
	{ return pV.Times(this.Dot(pV) / pV.LenSqr()); }

	// cosine of the angle between two Vec3Ds:
	public double CosAng( Vec3D pV)
	{ return this.Dot(pV) / (Length() * pV.Length()); }

	// comparison
	public boolean equals( Vec3D pV)
	{ return x==pV.x && y==pV.y && z==pV.z; }

	public boolean notEquals( Vec3D pV)
	{ return x!=pV.x || y!=pV.y || z!=pV.z; }

	// input/output

	public String toString()
	{ return "(" + this.x + "," + this.y + "," + this.z + ")"; }
}