Preheat your oven to 350°F (175°C). Grease a loaf pan and set aside.
In a mixing bowl, whisk together the flour, baking powder, and salt.
In another bowl, combine the yogurt, sugar, eggs, lemon zest, and vanilla extract.
Slowly whisk the dry ingredients into the wet ingredients.
Fold in the vegetable oil until well combined.
Pour the batter into the prepared loaf pan and bake for about 45 minutes, or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.