Sum of Spacelike Vectors: Always Spacelike?

[ehrenfest]

Homework Statement

Is it true that the sum of any two spacelike vectors is spacelike? I spent forever on this problem (5.4 from the link) and I think not...
http://books.google.com/books?id=xm...ts=aowTGAbHj6&sig=EIQ6_W2eCQmMnHVP0l6FH2dEehg

Actually, I think it is clearly not true if you think about the light-cone. But go to the link and tell me if there is something I am missing.

Homework Equations

The Attempt at a Solution

 

[Dick]

It is very true that the sum of two spacelike vectors is not necessarily spacelike. Like, (t,x)+(t,-x)=(2t,0) where (t,x) is spacelike. It's not clear to me what the author is thinking about.

 

[Meir Achuz]

He must mean in the same direction. In any event it is a silly problem for a GR book.