Here is ur answer mate

Since a person is moving towards North for 3km

• Direction of movement - North

therefore ↑North - 3km

Now the person turns to walk 4km further

• Direction of movement - WEST

therefore ↑North - 3km

and ←West - 4km

Now the person walks 3km after turning right

• Direction of movement - North

therefore ↑North - 3km + 3km = 6km

and ←West - 4km

In the end the person turns right again and moves forward the 12KM in EAST direction

• Direction of movement - East (opposite to West)

Therefore ↑North - 6km

and ←West - (4km - 12km) = -8KM

Here we get West direction in negative

therefore we will replace it by East and -8km by its ADDITIVE inverse i.e 8km

Therefore ↑North - 6km

→ East - 8km

Here a formation of a right triangle can be observed....

Where 8km and 6m are lengths of its legs

Therefore by Applying Pythagoras theorem

(Displacement)² = (Northen Displacement)² + (Eastern Displacement)²

or (Displacement)² = (6km)² + (8km)²

= 36km² + 64km²

= 100km²

or Displacement = √(100km²)

= 10km