Heat the oven to 350°F. Grease a 4-1⁄2 x 8-1⁄2-inch loaf pan with unsalted butter or nonstick cooking spray.
In a large bowl, whisk together the flour, baking powder, baking soda, and salt until well combined. Stir in the dried apricots. Make a well in the center and set aside.
In a medium bowl, using a wire whisk, lightly beat the eggs. Add the sugar and whisk until smooth. Gradually whisk in the oil until well blended. Whisk in the orange juice and vanilla. Stir in the orange zest.
Pour the liquid mixture into the well in the center of the flour mixture and stir until combined. Spoon the batter evenly into the prepared loaf pan.
Bake until golden brown and a wooden pick inserted in the center comes out clean, 50 to 60 minutes. Remove the pan from the oven and immediately remove the bread from the pan. Turn the loaf on its side and let cool on a wire rack.