In what sense does this vector "converge" to zero?

From: K Yee (kentonyee_at_hotmail.com)
Date: 11/26/04 

Date: 26 Nov 2004 03:34:20 -0800

Let M be an nxn symmetric positive semidefinite matrix.
Suppose v is an n-tuplet that satisfy 2 conditions (only)
in the limit that n goes to infinity:
   v' v -> 1
   v' M v -> 0.

(i) Let w = M v.
Do the 2 conditions on v imply that in the n->infinity limit
     w -> 0?
(ii) If (i) is not true, is it true that
     w' w is finite or zero in some sense?

Thanks in advance!
Rod

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