How do I apply direction to a velocity?

I want to make a part fly off towards the direction it's facing when a player touches it. I can get the direction with lookVector, but how would I apply that to something, like BodyVelocity?

Velocity is both the speed and the direction of a Part. lookVector is also a direction, so you can set it directly:

part.Velocity = part.CFrame.lookVector * bigNumber

You need to multiply it by a big number so that it will have more speed.

Here's some code for a missle from a plane - basically BodyVelocity.velocity is set to the lookvector of a part and multiplied by the speed you want it to go forward.

function FireMissile(Gun) --This function creates the non-guided missiles for the missile spawns
	if (not Locked) then
		local Exploded = false
		local Part1 = Instance.new("Part")
		Part1.Name = "Missile"
		Part1.CanCollide = false
		Part1.FormFactor = "Symmetric"
		Part1.Size = Vector3.new(1,1,5)
		Part1.BottomSurface = "Smooth"
		Part1.TopSurface = "Smooth"
		local Mesh = Instance.new("SpecialMesh")
		Mesh.Parent = Part1
		Mesh.MeshId = "http://www.roblox.com/asset/?id=2251534"
		Mesh.MeshType = "FileMesh"
		Mesh.TextureId = "http://www.roblox.com/asset/?id=2564491"
		local Part2 = Instance.new("Part")
		Part2.Parent = Part1
		Part2.Name = "Visual"
		Part2.Transparency = 1
		Part2.CanCollide = false
		Part2.FormFactor = "Symmetric"
		Part2.Size = Vector3.new(1,1,1)
		Part2.BottomSurface = "Smooth"
		Part2.TopSurface = "Smooth"
		local Weld = Instance.new("Weld")
		Weld.Parent = Part1
		Weld.Part0 = Part1
		Weld.Part1 = Part2
		Weld.C0 = CFrame.new(0,0,5)*CFrame.Angles(math.rad(0),0,0)
		local BV = Instance.new("BodyVelocity")
		BV.Parent = Part1
		BV.maxForce = Vector3.new(math.huge,math.huge,math.huge)
		local BG = Instance.new("BodyGyro")
		BG.Parent = Part1
		BG.maxTorque = Vector3.new(math.huge,math.huge,math.huge)
		BG.cframe = Gun.CFrame * CFrame.Angles(math.rad(0),0,0)
		local Fire = Instance.new("Fire")
		Fire.Parent = Part2
		Fire.Enabled = false
		Fire.Heat = 25
		Fire.Size = 30
		local Smoke = Instance.new("Smoke")
		Smoke.Parent = Part2
		Smoke.Color = Color3.new(40/51,40/51,40/51)
		Smoke.Enabled = false
		Smoke.Opacity = 1
		Smoke.RiseVelocity = 25
		Smoke.Size = 25
		local PlaneTag = Instance.new("ObjectValue")
		PlaneTag.Parent = Part1
		PlaneTag.Name = "PlaneTag"
		PlaneTag.Value = Plane
		Part1.Touched:connect(function(Object)
			if (not Exploded) then
				if (not Object:IsDescendantOf(Character)) and Object.Name ~= "Missile" then
					Exploded = true
					local Explosion = Instance.new("Explosion")
					Explosion.Position = Part1.Position
					Explosion.BlastPressure = 50
					Explosion.BlastRadius = 5
					ScanPlayers(Part1.Position,5)
					Explosion.Parent = game.Workspace
					Part1:Destroy()
				end
			end
		end)
		Part1.Parent = game.Workspace
		Part1.CFrame = (Gun.CFrame * CFrame.Angles(math.rad(0),0,0)) + Gun.CFrame.lookVector * 15
		BV.velocity = Part1.CFrame.lookVector * Engine.Velocity.magnitude
		delay(.03,function()
			BV.velocity = (Part1.CFrame.lookVector * 1000) + Vector3.new(0,0,0)
			Fire.Enabled = true
			Smoke.Enabled = true
		end)
		delay(5,function() Part1:Destroy() end)
	end
end

Speed and Direction and both controlled by the velocity. here's and example

function fire(d)
Part.Position = script.Parent.Part.Position + (d*5)
Part.Velocity = d*100
end

so the *5 is how far it will be pushed from the part(not how far overall) and *100 is how fast it will be pushed higher the number faster it goes.