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a boat starts at point A, moves 3km due north, then 2 km due east, then 1 km due south, and then 4 km due east to point b. Find the distance AB

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Add up each component (north or east) separately, and finally find the distance by the vectorial sum (using Pythagoras).

North: 3-1=2km
East: 2+4=6
Distance = √(2²+6²)
=√(40)
=2√(10)

• Math -

I don't understand where for North you put 3-1. The boat moved 1km South and 3km North. Is that how this was done?

• Math -

In vectors, directions are signed.

This means that if we take the positive direction as north, then going south is backwards, and is thus represented as negative. Otherwise it would not make a difference between going 3 km north and 1 km north (3+1), and going 3 km north and 1 km south (3-1).

Hope that clarifies how it's done.

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