I have been told that vitamin K may be administered subcutaneously but should not be administered intravenously in adults. If this is correct then why is this so?

See answer. In order of highest to lowest preference, vit k can be given orally (po), subcutaneously (sq), intramuscular (im), or intravenous (iv). The injectable form of vitamin k can rarely cause severe (sometimes fatal) allergic reactions when given by im or iv. Therefore, vitamin k should only be given im or slowly IV if rapid or immediate correction of over-anticoagulation is required.
Risk of anaphylaxis. If given iv, there is a risk of an anaphylactic reaction (life-threatening allergic reaction). Vitamin k generally is given by an intramuscular or im injection. If given iv, it should be infused very slowly, while monitoring closely for any adverse reaction.