Vector proof - four points in space

[nc01]

The problem is: A, B, C, D are any four points in space. If M and N are the mid-points of AC and BD, show that AB + CB + CD = 4MN.

I'm not quite sure where to start. Could someone please help me?

 

[flatmaster]

I'm not sure that the problem is correct. Suppose that A,B,C,D are the four corners of a square. In this case, M and N would both be the center of the square. This would make MN=0

 

[tiny-tim]

welcome to pf!

hi nc01! welcome to pf!

The problem is: A, B, C, D are any four points in space. If M and N are the mid-points of AC and BD, show that AB + CB + CD = 4MN.

??

i think you need an AD in there …

AB + AD + CB + CD = 4MN ​