Vectors in 2D describes scalar and vector quantities. Scalar quantities only have magnitude, while vector quantities have both magnitude and direction. The document explains that two ships sailing the same distance but with different bearings will not end up at the same place, and an airplane traveling the same speed but in different directions will also not reach the same destination. It also demonstrates how to find the magnitude of a vector using the Pythagorean theorem and defines two vectors as equal if they have the same magnitude and direction.

1. Vectors in 2DAdditional Mathematics

2. Quantities which have only magnitudes are called SCALAR QUANTITIESAreaDistanceTime

3. Will a ship sailing 8 km on a bearing of 075 get to the same place as one sailing 8 km on a bearing of 165?N075°165°

4. Will an aeroplane going at 750 km/h north get to the same place as one going at 750 km/h east?North750 km/hEast750 km/h

5. Quantities which have both magnitudes & directions are called VECTOR QUANTITIESNNorth750 km/h075°East165°750 km/h

6. The displacement of the ship from P and Q is represented by directed line segmentNDisplacement:Magnitude:(Length of PQ)Q8 kmP

7. Column Vector & Its MagnitudeThe displacement from S to T can be achieved by moving 6 units to the right and 7 units upT7 unitsuBy Phytagoras’ theorem, the magnitude of the vector is given byvS6 units

8. Column Vector & Its MagnitudeColumn VectoravMagnitudeu

9. Two vectors are equal if they have the same magnitude and the same directionrpDBqACWhich vectors are EQUAL?

10. On its return journey, the ship sails 8 km from Q to P on a bearing 255°.NN-a075°QQ255°aPP