Do the Pact of the Blade warlock's Eldritch Smite and Lifedrinker eldritch invocations work with ranged pact weapons?

Question

It is possible for a Pact of the Blade warlock to have a ranged weapon as a pact weapon.

The description of the Improved Pact Weapon eldritch invocation (XGtE, p. 57) includes the following:

Finally, the weapon you conjure can be a shortbow, longbow, light crossbow, or heavy crossbow.

If a warlock has a ranged pact weapon, can they enjoy the benefits of the Eldritch Smite and/or Lifedrinker eldritch invocations, or do they only work with melee pact weapons?

On the one hand, they don't say anything about melee weapons, but on the other hand, the word "hit" makes me think of physically striking the target creature. Which interpretation is correct?

Lifedrinker (PHB, p. 111) says:

When you hit a creature with your pact weapon, the creature takes extra necrotic damage equals to your Charisma modifier (minimum 1).

Eldritch Smite (XGtE, p. 56) says:

Once per turn when you hit a creature with your pact weapon, you can expend a warlock spell slot to deal an extra 1d8 force damage to a target, plus another 1d8 per level of the spell slot, and you knock the target prone if it is Huge or smaller.

Answer 1

"Hit" is the general term used for "You made an attack roll and equalled or beat the target's AC".

So this would work just fine. If an ability was restricted to being used only with Melee weapons (or ranged ones) then the text would mention this directly by saying something like:

"When you hit a creature with a melee weapon attack" or "When you hit a creature with a melee attack using your Pact Weapon", but it does not.