With an electric mixer or by hand, beat together the eggs and sugar until thick. Gradually beat in the oil.
Stir in the flour, baking powder and salt, and then the orange juice. Beat until smooth, and then mix in the zest and vanilla.
Pour the batter into your prepared pan, and bake for about 40 minutes, or until the cake tests done.
Allow the cake to cool in the pan for 7 to 10 minutes, then turn out onto a rack to finish cooling