Preheat oven to 350 degrees.
In a large bowl, whisk together the dry ingredients. Stir in the eggs, oil, and vanilla.
Fold in the pineapple, pecans, and bananas.
Pour into greased and floured cake pans about half full.
Bake for 45 minutes to 1 hour, or until a toothpick inserted in the center comes out clean.
Cool in the pans for 10 minutes, then turn out on a wire rack to cool completely.
If possible, wrap and refrigerate overnight. It makes frosting the cake easier!