Question
I was wondering,
How do Plants absorb vitamins?
           and
What Is The Effect Of Different Vitamins(Vitamin A, C, D, E,) On Plant Growth?

                       thanks

Answer
Plants do not need vitamins, like people, but a different sets of nutrients.

Plants actually manufacturer their own food from carbon dioxide, oxygen, and water plus a number of nutrients they extract from the soil.

The nutrients they extract from the soil are:

Macro Nutrients:
Nitrogen, Phosphorus, Potassium, Sulphor, Magnesium, and Calcium

Micro Nutrients:
Chlorine, Iron, Manganese, Zinc, Copper, Boron, and Molybdenum.

Plants need all nutrients to grow, no one being more or less important. However, the plants consume larger quantaties of the macro nutrients compared to the micro nutrients.

Boron for example is only needed in 1/1000 of a gram whereas several ounces of nitrogen may be consumed by a large tree, for example. Plants need all 13 nutrients from the soil, but some are required in larger quantaties than others.

Outdoors, in soil, the micro nutrients are usually available in soil, e.g. do not need to be supplied by the farmer or gardener, although in some cases individual nutrients such as iron or boron may be lacking. The average home gardener seldom have to worry about these but professional nursery growers and farmers do add these based on a soil test (an analysis of what the soil already contains).

The 3 larger nutrients: N-P-K:  Nitrogen, Phosphorus, and Potassium are commonly supplied through the use of FERTILIZERS.

A fertilizer is simply a SALT (e.g. like table salt you use for preparring foods), but instead of being sodium chloride (NaCI) it may be other types of salts such as potassium nitrate, ammonium nitrate, etc.

These fertilizer salts are so-called IONIC compounds, e.g. they consist of two or more molecules which has a negative or positive charge. Think of it as two magnets holding together (the positive end of one magnet attract the negative end of the other magnet).

When placed in water, these molecules are pulled apart by the water molecules, and each molecule are now "floating" in water seperately.

Example: Table salt for example. Sodium Chloride consist of a large positive charged Sodium molecules which bonds strongly with a negatively charged Chloride molecule. When placed in water the water molecules will literally pull these two atoms apart. E.g. they are no longer bound strongly together.
Think of it, as if the Sodium molecules now floated around in water seperate from the Chloride molecules.

Plants have small fine hairs at the end of their roots which are very efficient at extracting water and other small molecules. These molecules enter a fine membrane, e.g. like a screen, and can pass through to the roots. The large, combined, table salt molecule (sodium choloride, NaCI) would be too large to pass this screen, but individually, as a sodium and chloride molecules these nutrients can enter then plants.

As you may understand, the fertilizer nutrients are therefore made available to the plants by being dissolved in water first. This is actually one of the reasons why plants need water. Without water, the fertilizer nutrients would be too big to pass into the roots.

In nature, plants find these fertilizer nutrients as part of the soil and are made available to the plants when the soil is wet. Othertimes, gardeners may supply these nutrients by applying fertilizer, either as inorganic factory produced material, or as natural organic fertilizer (such as cow manure, bone meal, dried blood, compost, etc).

If applied as organic material (such as compost), the fertilizer nutrients are usually not available in a form which the plants can utilize. The nutrients are usually locked in larger complex molecules. However, the constant activity by microbes in the soil help to break apart these larger molecules into inorganic compounds (such as nitrates for example) which can then be dissolved in water and taken up through the plants.

So, to answer your question ...

plants do not absorb vitamins as  such and do not need the same vitamin a,c,d,e etc as we do. Some nutrients, sodium, potassium, etc we have in common.

In order for plants to absorb these nutrients, microbes in the soil must first convert these nutrients into inorganic ionic compounds which can be dissolved in water. At this time, they enter the plant through fine hairs on the roots.

Inside the plants, these nutrients are combined with water and carbon dioxide to form sugars (sucrose) which the plant uses to manufacture stem, leaves, fruits, and flowers. E.g. the plants actually make their own food from individual molecules.

The largest nutrients sources (hydrogen, carbon, oxygen) the plants derrive directly from the carbon dioxide and water.

Of the nutrients which the plants take up through the soil, the larger ones (macro nutrients) are responsible for following key functions:

Nitrogen (N) is responsible for building DNA and proteins. It is a key building block for the green material.

Phosphorus (P) is essential for photosynthesis in plants (e.g. the plants ability to be able to convert the sun's energy into energy).

Potassium (K) regulates how water is taken up in cells, e.g. the ability of plants to stay upright for example.

Sulphor (S) is responsible for good growth and seed production.

Calcium (Ca) plays a role in cell elongation and cell structure.

Magnesium (Mg) help manufacture enzymes and also plant chlorophyll which is what you see as 'green' on a plant.

As mentioned, all the nutrients (macro as well as micro) are needed, they are just needed in different quantities.