Can the projection of w onto v point in the opposite direction of v ?
Yes, as it did in that example.
The diagram shows:
w = (4, 2.5, 2.5)T — red vector
v = (5, 0, 3.1)T — green vector.
Mentally project w onto v. (Hint: remember that the length of v does not matter; only its orientation. So mentally "drop" the arrowhead of w onto the dotted line).