Your racquet can cross the net as long as it never touches it. This does not mean you can just start reaching across the net to hit balls before they come to your side. Before you can hit a return, the ball must first cross over the net to your side of the court. (ITF Rule 24)
Can your racket go over the net in tennis? Yes it can, but only if the initial contact is made on your side of the court. If you do this and the racket crosses over the net as part of the follow through on your swing, that’s fine. You just have to ensure you don’t touch the net at any point. ITF Rules Of Tennis Rule 25e
Ordinarily, you are not allowed to reach over the net to hit the ball in tennis. Your racquet may cross over the net as long as you make contact with the ball on your side of the net, though. You or your racquet cannot touch the net at all or you lose the point. There are rare cases when you are allowed to reach over the net without losing the point, however.
This is why you see players running at a diagonal; to avoid the net or to avoid crossing over that imaginary net/extension. This is the only exception allowed. At low levels of tennis, if you stick your racquet over the net while the point is live, you have invaded your opponent's court/playing area.
If the spin or wind brings the ball back over the net to the side of the player (s) who hit the shot, the opponent (s) may then reach over the net and play the ball. They may not touch the net or the opponent’s court. This is the only situation when a player may reach over the net to play a ball.
(There has never been any rule in table tennis which stopped you from hitting the ball on your opponent's side of the net, but I understand that there used to be a rule in tennis which said your racket could not pass over the net).
In this case, to win the point, a player must reach over the net and hit the ball before it lands. However, if while doing so the player touches the net or if the ball lands (on the opponent’s ...
The rule states that when a ball fails to clear the net, or bounces in any spot other than the cross-court service box, it’s a fault. The game stops completely after a fault to contemplate the next action. This is the first fault, so the player is given a second chance.