Guys, if you ever need to grind out reputation for Vanguard or any of the factions (outside of crucible), i saw a tactic online today that works really well.
gather a fireteam and go to earth and complete patrols. Patrols give you rep but here's the kicker. With 3 members you all scatter to different locations on earth and complete the patrols in that area on your own. The whole fireteam gets the rep for each completion.
You should pick patrol missions that keep you in the area you currently occupy, this way you don't have to travel to complete.
Check gothalion's video below for more info on how you can see from your ghost what type of mission you get when looking at the mission beacons.