Doug plants a few peas. after two days, he sees the shoot and the root forming. he observes that the shoot grows upward, toward the light. the root grows downward, into the soil. why do these embryonic organs grow in a specific direction?

The shoot is used to collect sunlight for photosynthesis, so the genetic programming (as I like to call it), told the plant to grow toward the light, and the light was upward. The roots are programmed to obtain nutrients from the soil, like water, so the roots were growing downward to collect more water.

Gay-lussac's law i think.