Can the projection of w onto v point in the opposite
direction of v ?

A good answer might be:

Yes, as it did in that example.

Example in Three Dimensions

The diagram shows:

w = (4, 2.5, 2.5)^{T}
— red vector

and

v = (5, 0, 3.1)^{T}
— green vector.

QUESTION 14:

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).