A plane flies at 400 km/h, another at 300 km/h, and a third at 500 km/h. Draw a scale diagram (1 cm = 200 km) showing their positions after 3 hours.

The formula for distance is $\text{Distance} = \text{Speed} \times \text{Time}$.
Time elapsed for all planes is 3 hours.

For Plane A:

$$\text{Distance}_A = 400 \text{ km/h} \times 3 \text{ h} = 1200 \text{ km}$$

For Plane B:

$$\text{Distance}_B = 300 \text{ km/h} \times 3 \text{ h} = 900 \text{ km}$$

For Plane C:

$$\text{Distance}_C = 500 \text{ km/h} \times 3 \text{ h} = 1500 \text{ km}$$

The given scale is $1 \text{ cm}$ represents $200 \text{ km}$.
To find the length on the drawing, divide the actual distance by the scale factor ($200 \text{ km/cm}$).

For Plane A:

$$\text{Length}_A = \frac{1200 \text{ km}}{200 \text{ km/cm}} = 6 \text{ cm}$$

For Plane B:

$$\text{Length}_B = \frac{900 \text{ km}}{200 \text{ km/cm}} = 4.5 \text{ cm}$$

For Plane C:

$$\text{Length}_C = \frac{1500 \text{ km}}{200 \text{ km/cm}} = 7.5 \text{ cm}$$

To show the relative positions of the three planes, follow these steps:

1. Mark a point P in the center of your paper to represent the airport.
2. Draw a vertical line upwards from point P. This line represents the North direction.
3. For Plane A:
   • Using a protractor, measure an angle of $070^\circ$ clockwise from the North line at point P.
   • Draw a line segment from P along this $070^\circ$ bearing, with a length of 6 cm. Label the end of this segment as A.
4. For Plane B:
   • Using a protractor, measure an angle of $162^\circ$ clockwise from the North line at point P.
   • Draw a line segment from P along this $162^\circ$ bearing, with a length of 4.5 cm. Label the end of this segment as B.
5. For Plane C:
   • Using a protractor, measure an angle of $290^\circ$ clockwise from the North line at point P.
   • Draw a line segment from P along this $290^\circ$ bearing, with a length of 7.5 cm. Label the end of this segment as C.
6. Clearly indicate the scale used on your drawing: $1 \text{ cm} = 200 \text{ km}$.

The lengths to be drawn for each plane are:
Plane A: $\boxed{\text{6 cm}}$
Plane B: $\boxed{\text{4.5 cm}}$
Plane C: $\boxed{\text{7.5 cm}}$