A projector including an exterior enclosure, a light source apparatus, a light modulator, a projection optical apparatus, a plurality of detection light radiators that radiate detection light used to detect a pointing element onto a projection area, an imager that receives light that belongs to a wavelength region including the wavelength of the detection light to capture an image of the projection area, and a position detector that detects the position of the pointing element in the projection area based on the image captured by the imager, wherein the plurality of detection light radiators are arranged in different positions on the exterior enclosure, the plurality of detection light radiators include a first detection light radiator, and the first detection light radiator is so configured that a distance therefrom to another detection light radiator out of the plurality of detection light radiators is changeable.