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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

  • Math -

    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)

  • 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.

  • Math -

    similar to other

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