These two words are the last two of the formula of a "birkat mitzvah," the brakhah that is recited before performing a commandment. They both come from the same root. If we clear away the prefixes and suffixes, it will be easier to see how they relate.
"B" means in or with. "Av," as a suffix, means "his." Take them both away and you are left with "mitzvot," commandments. More on that word in a moment. Right now, the important thing is to translate "b'mitzvotav" as "with his commandments."
"V" in front of a word means "and." And we have already learned that "-anu" means "us" at the end of a word (as in "kid'shanu"). Take them both away and you are left with "tziva," the verb form of the noun "mitzvot." It means "commanded." The word "v'tzivanu" means "and commanded us."
Rather than focusing on the meaning of the word "command," I prefer to focus on its implications. As many scholars have noted long before me, if the command exists, there must be a commander. The usage of the word "mitzva" has strayed from the sense of commandment; colloquially it has come to mean a good deed. But the combination of "b'mitzvotav v'tzivanu" does not allow us to avid the implications of the true meaning. God has mandated a certain set of behaviors.
It is at this moment in the brakhah that the varieties of theology run into a dilemma. We can interpret and explain away all of the other words that precede these two, including the very names of God. But when we arrive at "with His commandments and commanded us," there is no honest implication of those words other than the existence of a commander. Having laid the groundwork for our theological statement -- God's power, compassion, judgment, universality, sanctification – the brakhah formula makes us ask and answer Judaism's essential question: why are we doing what we do? Because God said so.
The answer to the question does not sit well with independently-minded liberal Jews. It sounds so, so...religious! But we have presumed to call on God's name and to call on God's presence. We have shaped these words to make us feel worthy and able to speak about God and to God. Now is the time for a dose of humility. We may have selected the words, but we did not create the ideas behind the words.
As an antidote to our humble pie, a glimmer of affirmation appears. If we have been commanded by God, then we have been called into meaningful relationship. God cares enough about us to help shape our actions.
We have reached the end of the common words of the brakhah. Next time, a few words about the chatima, the concluding words of the brakhah. And then onto something different!
PLEASE NOTE THAT THERE WILL BE NO POSTINGS ABOUT PRAYER TO THIS LIST DURING THE WEEK FOLLOWING EACH OF THE HOLIDAYS.