jq extracting properties to arrays from json row line

For example if we have a file that contains JSON object like

{"a": 1, "b":{"c": 11}
{"a": 2, "b":{"c": 22}}
{"a": 3, "b":{"c": 33}}

And you want to construct something like

["1", "11"]
["2", "22"]
["3", "33"]

You can do that with jq

$ cat filename.json | jq -c '[.a, .b.c]'

this is particularly usefull to grep something from JSON log