I have bought vitamin D3 drops and have been adding two drops to a plate of food before we eat it. Will it have the same effect if I add it to the whisked eggs and then cook the omelette or is the vitamin denatured by the cooking?
The vitamins most depleted by heat are the water-soluble ones, namely C, & B vitamins. D belongs to a category of fat-soluble vitamins and so is more heat-stable; looking at studies on foods fortified with vitamin D (namely cheese), it was found that it was not significantly affected by heat (processes such as pasteurization and cooking). And, just on an aside, you cannot 'denature' a vitamin, since it isn't a protein, though denaturation of proteins can deplete some vitamins therein :-)
However, isolated vitamin D will definitely be more unstable: cholecalciferol (D3) is sensitive to UV light which makes it break down into sterols; it is also highly unstable at temperatures above 40 degrees Celcius and humidity above 45 % - storing at these conditions showed significant depletion and chemical degradation.
However, the vitamin D drops are not just pure Cholecalciferol; the vitamin is contained in some sort of base and the formula will definitely contain stabilisers and antioxidants which prevent degradation. So very much depends on the particular formula you are using: read the label/leaflet, perhaps there are recommendations on there - I think that if the manufacturer knew the formula was heat-sensitive there would be a warning on the bottle not to add to hot foods.
In general, I think its ok to add to cooked/warm/hot food - I found this - http://vitaminddrops.com/adult-faq.php - this is probably a different brand to which you are using, but it does say that the drops are ok to add to food & drink after cooking. Note that they recommend not to add it to raw food before cooking: fat-soluble vitamins are still depleted to an extent even when contained in whole foods; the isolated vitamin, even if it is protected by stabilisers, will be slightly more sensitive to heat, and so the quantity will decrease, and if you're taking a supplement, you want to know you're getting the full designated dose.
So stick to adding it after cooking to tolerably hot food (so I'd even recommend to wait for it to cool down to edible temperature if its piping hot, before adding the drops). And even though you supplement, do eat vitamin D -rich foods such as oily fish, and get as much sunlight as you can, since vitamins from whole foods are most effective than ones taken in isolation.
Lots of love