There are several different plant hormones. Those controlling the growth of roots and shoots are called auxins which stimulate cell growth.
Auxins can diffuse from cell to cell in solution or travel greater distances in the plant in the vascular bundles.
If a plant has light falling on it from one side only, it will grow towards the source of the light. This is as a result of auxin accumulating on the side of the plant away from the light, causing extra growth in this region and so causing the plant to bend towards the light.
Roots are not sensitive to light but grow downwards in response to the stimulus of gravity. Auxins are again involved, although scientists think another plant hormone might actually cause slowing of the growth of cells on one side of the root causing it to bend downwards.
Plants hormones are used widely in agriculture in the following ways: