The Old Testament focuses on Gods power and shows how that power is used to strengthen the faith of His believers. When God seeks out revenge against sinners, nonbelievers, and those who persecute His followers it gives hope to His followers to continue to follow in His ways. Sinners also serve as an example for what will happen if Gods followers sin and fail to obey His word.
Psalm 79 mourns the fall of Judah to Babylon and the destruction of the temple. The people call on God to avenge his people and strike down the enemy for the sake of his name. (The "enemy" refers to all nonbelievers that are tormenting and persecuting Gods followers.) "Pour out your anger on the nations that do not know you, and on the kingdoms that do not call your name." This passage makes the reader come to the conclusion is acceptable and almost expected that God will seek revenge on those who hurt His people. "Let the avenging of the outpoured blood of your servants be known among the nations." Towards the end of the Psalm it discusses how the people will praise God for taking this revenge. Almost implying that by God avenging his people he is proving his love and devotion for them, and in doing so He strengthens the peoples faith in Him.
In Numbers 35 it discusses the issue of homicide and when it is and when it is not allowed for one to avenge the murderer. It says that if you kill with intent then the avenger has the right to kill the murderer. "If someone pushes another from hatred, or hurls something at another, lying in wait, and death ensuesthen the one who struck the blow shall be put to death." But, if the murder was committed unintentionally than no one has the right to avenge the killer. However, even these who have killed without intent are liable to punishment unless a few stipulations are followed. First, the murderer must remain in the city of refuge until the high priest dies, because the high priest's death is what cancels the bloodguilt of the murderer. If the murderer does not obey this law and leaves the borders of the city of refuge before the death of the high priest then the avenger does have the right to kill the murderer. Second, if only one person is witness to the murder then the killer cannot be put to death. But if there is more than one witness then the murderer can and will be put to death. "If anyone kills another, the murderer shall be put to death on the evidence of witnesses; but no one shall be put to death on the testimony of a single witness."
Jeremiah 15. 15-18 asks the Lord to strike down those who do not obey Him for they persecute His followers and make them miserable. "Bring down retribution for me on my persecutorsknow that on your account I suffer insult." Jeremiah complains that he does everything the Lord asks him to, believes all the words the Lord preaches, he even refrains from rejoicing with the "merrymakers" (sinners) and yet he is still in pain here on earth. "Under the weight of your hand I sat alone,Why is my pain unceasing,Truly, you are to me like a deceitful brook, like waters that fail." Jeremiah feels that if this revenge is not taken the Lord is not proving His love for His followers and consequently Jeremiah feels betrayed because of Gods lack of action. In other words, the Lords punishment of sinners is a strengthener of faith for His believers.