engage vs vow

engage

verb
  • To guarantee or promise (to do something). 

  • To enter into conflict with (an enemy). 

  • To come into gear with. 

  • To enter into (an activity), to participate (construed with in). 

  • To draw into conversation. 

  • To mesh or interlock (of machinery, especially a clutch). 

  • To attract, to please; (archaic) to fascinate or win over (someone). 

  • To engross or hold the attention of; to keep busy or occupied. 

  • To arrange to employ or use (a worker, a space, etc.). 

  • To bind through legal or moral obligation (to do something, especially to marry) (usually in passive). 

  • To enter into battle. 

vow

verb
  • To make a vow; to promise. 

  • To declare publicly that one has made a vow, usually to show one's determination or to announce an act of retaliation. 

  • To make a vow regarding (something). 

noun
  • A solemn promise to perform some act, or behave in a specified manner, especially a promise to live and act in accordance with the rules of a religious order. 

  • A declaration or assertion. 

How often have the words engage and vow occurred in a corpus of books? (source: Google Ngram Viewer )