A tourist drives 10 km towards east and turns to the right hand and drives 3 km. Then he drives towards west (turning to his right) 3 km. He then turns to his left and drives 2 km. Finally he turns to his right and travels 7 km. How far is he from his starting point and in which direction with respect to starting point?

The tourist's journey can be broken down into the following steps:

1. He drives 10 km east.
2. He turns right (which would be south if he was facing east) and drives 3 km.
3. He turns right again (which would be west if he was facing south) and drives 3 km.
4. He turns left (which would be south if he was facing west) and drives 2 km.
5. He turns right (which would be west if he was facing south) and drives 7 km.

Now, let's calculate the total distance he has traveled in each direction:

• East: 10 km (initial drive) - 3 km (third step) = 7 km
• South: 3 km (second step) + 2 km (fourth step) = 5 km
• West: 7 km (final step)

So, the tourist is 7 km west and 5 km south of his starting point.

To find the straight-line distance from his starting point, we can use the Pythagorean theorem, which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the "hypotenuse" is the straight-line distance we're trying to find.

So, the straight-line distance is √((7 km)^2 + (5 km)^2) = √(49 km^2 + 25 km^2) = √74 km^2 = approximately 8.6 km.

As for the direction, we can use the arctangent function to find the angle between the east direction and the line connecting the starting point and the final position. The arctangent of the opposite side (5 km south) over the adjacent side (7 km west) is approximately 35.5 degrees. This angle is measured counterclockwise from the east direction, so the final direction is south of west.

So, the tourist is approximately 8.6 km from his starting point, in a direction 35.5 degrees south of west.