Question

A vector that is 1 cm long represents a displacement of 21 km. How many kilometers are represented by a 3-cm vector drawn to the same scale?

Answer 1

The 3 cm vector represents 63 km.

Since a 1 cm long vector represents a displacement of 21 km, we need to find the number of kilometers a 3 cm vector represents.

Let x represent the displacement the 3 cm vector represents.

By ratio, we have 1 cm: 21 km = 3 cm : x

So, 1 cm/21 km = 3 cm/x

Cross-multiplying, we have

x × 1 cm = 3 cm × 21 km

x = 3 cm × 21 km/1 cm

x = 63 km

So, the 3 cm vector represents a displacement of 63 km.

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