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Exactly! The magnitude of both vectors is \(20\), whereas the directions are different because the angles they are making with the positive x-axis are different.
Imagine two cars: a Mercedes and a Rolls-Royce. Both of them are travelling at \(100 \, \mathrm{km/h}\). But, the Merc is going towards the East, and the Rolls-Royce is going towards the West.
If the car's motion can be thought of as a vector, what is true about the Mercedes vector and the Rolls-Royce vector?
  • A and B have the same direction, but, different magnitudes
  • A and B have the same magnitude, but, different directions
  • A and B have different magnitudes and different directions
  • A and B have the same magnitude and direction