That depends on the size, YT. Tiny baby carrots or small cukes are OK whole. Otherwise, you need to slice them, either crosswise, diagonally, or into sticks. Other possibilities are cauliflower florets, whole baby okra, sliced green tomatoes, blanched green beans, or any kind of pepper.
By the way, the cauliflower florets go great with pickle beets. It turns a beautiful shade of bright pink that makes a great accent for an antipasto plate.
I think you should check out the some other recipes...Some vegies require special treatment. For instance, sliced cukes are usually salted and covered with ice before pickling.
My favorite sweet brine is:
1 cup water
1 cup white vinegar
1 cup sugar
1 tbl mixed pickling spice (optional)
Mix all, bring to boil, reduce heat and simmer for 20-30 minutes. Pour hot liquid over prepared vegies in jars, seal and can in boiling water bath or refrigerate.
If you want a salty one, search out my post "pick a peck'a pickled peppers" on the canning forum.