Question

A vector that is 1cm long represents a displacement of 5km. How many kilometers are represented by a 3cm vector drawn to the same scale?

Answer 1

A 3cm vector drawn to the same scale as a 1cm vector representing 5km would represent a displacement of 15 kilometers.

Step-by-step explanation:

To determine how many kilometers are represented by a 3cm vector drawn to the same scale, we use the given scale in the question. A vector that is 1cm long represents a displacement of 5km. This establishes a scale where 1cm corresponds to 5km.

Using this scale factor, we can find out how many kilometers a 3cm vector represents by multiplying the scale factor by the length of the vector in centimeters:

Scale factor: 1cm = 5km
Vector length: 3cm

To find the corresponding displacement in kilometers for the 3cm vector, we calculate:

5km/cm × 3cm = 15km

So, a 3cm vector drawn to the same scale represents a displacement of 15 kilometers.

Answer 2

A 3cm vector drawn to the same scale as a 1cm vector representing 5km would represent a displacement of 15 kilometers.

Step-by-step explanation:

The student asks how many kilometers are represented by a 3cm vector, if a 1cm vector represents 5km. This is a mathematics problem involving ratio and scale.

Firstly, we establish the scale being used: 1cm represents 5km. Therefore, the scale ratio is 1cm to 5km. To find out how many kilometers a 3cm vector represents, we multiply the length of the vector by the scale factor:

Length of vector in cm × Scale factor = Kilometers represented
3 cm × 5 km/cm = 15 km

Thus, a 3cm vector drawn to the same scale represents a displacement of 15 kilometers.