Sift together the flour, baking powder, and salt into one bowl. In another bowl, whisk together the yogurt, 1 cup sugar, the eggs, lemon zest, and vanilla. Slowly whisk the dry ingredients into the wet ingredients. With a rubber spatula, fold the vegetable oil into the batter, making sure it’s all incorporated. Pour the batter into the prepared pan and bake for about 50 minutes, or until a cake tester placed in the center of the loaf comes out clean.