On an open graound , a motor ist follws a track that truns to his left by an angle of ` 60^@` after every ` 500 m`. Starting from a given trun , specify the displacement of the motorist at the third, sizth and eighth turn. Compare the magniude of the dispalcembt with total path length coverd by the motorist in each case.

Explanation

To solve the problem step by step, we will analyze the motorist's movements and calculate the displacement and the total path length covered at the 3rd, 6th, and 8th turns.

### Step 1: Understanding the Movement
The motorist travels in a pattern where he makes a left turn of 60 degrees after every 500 meters. This creates a hexagonal path since the angle of each turn is 60 degrees.

### Step 2: Calculate Displacement and Distance for the 3rd Turn
1. **Path Covered**:
- The motorist travels 500 meters for each turn.
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