Destructive Smite and Vital Strike

[Riley Cooke]

I'm building an Inquisitor and was trying to figure out if I could stack the Destructive Smite ability from the Destruction domain with the Vital Strike feat.  Here's the description of both:

Destructive Smite (Su): You gain the destructive smite power: the supernatural ability to make a single melee attack with a morale bonus on damage rolls equal to 1/2 your cleric level (minimum 1). You must declare the destructive smite before making the attack. You can use this ability a number of times per day equal to 3 + your Wisdom modifier.

Vital Strike: When you use the attack action, you can make one attack at your highest base attack bonus that deals additional damage. Roll the weapon’s damage dice for the attack twice and add the results together before adding bonuses from Strength, weapon abilities (such as flaming), precision-based damage, and other damage bonuses. These extra weapon damage dice are not multiplied on a critical hit, but are added to the total.

[NikosBlu]

Well, it's pretty straightforward. Destructive smite is part of the attack action, regardless if it's a standard action, a full attack (only for a single attack, no matter how many you can make) or even a swift action, in the case of a Mythic character.
Vital Strike is an attack you make as a standard action, so the answer is:

Yes, you can use them both on the same attack. It might be a single attack per round, but it's gonna hurt like hell!