In any geological plane, strike gives the direction of a line formed by intersection of horizontal plane and geological plane. And dip shows the orientation of the geological plane. While studying, I came to know that strike is perpendicular to dip. But when I tried to determine dip from strike, I can not do it. But when I can determine strike when dip is known. So how can we determine dip if strike is known?
No. Strike is a line value whose direction is referenced with respect to true north. Dip can be any 0-90 degree angle (below horizontal) perpendicular to that line. It must be physically measured in the field....usually by some seriously underpaid graduate lackey.
Strike and dip are one way of describing the orientation of a plane in 3 dimensions. The strike is the angle of the intersection of the plane with a horizontal surface so the strike of a horizontal plane is undefined. Just as two intersecting lines define a point, two intersecting planes define a line. You can define a line perpendicular to the line of strike and this defines the direction of dip. If you imagine a vertical plane that intersects the horizontal surface along that line it will intersect your original geologic surface along another line. The angle between the direction of dip and the geologic surface is the dip angle, or just called the dip. Conventionally, the dip is always measured so it is the angle down from the horizontal.
If someone gives you a strike and dip, you still need one more piece of information to determine the orientation of the plane. That's because you need to know if the plane is dipping to your left or the right if you are looking in the direction of the strike. Some conventions specify the general direction of dip (e.g. to the east) but I prefer to use a convention where you define the strike direction so that your dip is to the right side (the right-hand rule) So if the strike is a line that points, for example 10 degrees (east of north) and 190 degrees (10 degrees west of south) and the dip is 30 degrees to the west you would say strike 190 degrees, dip 30 degrees. The dip is the maximum angle that can be measured between your geologic plane and the horizontal. Sometimes it is hard to tell if your are measuring the angle exactly down-dip and the value of that apparent dip will be less than the true dip.
Another way to describe the orientation of the same geologic plane is use the bearing and plunge (also termed plunge and azimuth). Go back to the vertical plane perpendicular to strike and its intersection with the geologic plane. Imagine looking along the line where that plane intersects the horizontal and facing down dip. That direction is the bearing (the strike plus 90 degrees if you are using the right-hand rule). The plunge is just the dip angle. The reason it is called something different is that you can use the same terminology to describe any linear feature such as the line where a bed intersects a fault.
I suspect that when you say, "dip shows the orientation of the geological plane" you mean both the dip angle (the plunge) and the bearing of the dip line. So in actuality you are still using two values with the bearing being 90 degrees from the strike. The reason you can't just use the strike is that that does not give you the angle value.
There is another way to define the orientation of a plane by defining the vector that is normal to the plane. That line forms an angle of 90 degrees with the line of dip. The convention in structural geology is to use the vector where the perpendicular to the plane points downward, not up in the air. The bearing and plunge of that vector is used to plot features on stereo-nets - a handy way to reduce the orientation of a number of planes to a number of points.