Distance Calculation using Vectors in 3D space

Mathematics has long been seen as a subject of logic, formulas, and problem-solving, yet for many students, it can feel like an intimidating or monotonous task. But what if math wasn’t just about solving equations on paper? What if it became an interactive, rewarding, and even fun experience? This is where gamification comes into play transforming traditional math problems into engaging challenges that spark curiosity and motivation.

The example below illustrates how to calculate distance using vector in 3D space

Let’s say we want to teach students about vectors in a fun and engaging way using gamification. Instead of giving them a set of equations to solve, we can turn it into a game like challenge.

Assume we have a submarine that sailed from the harbor to a location in the international water, this location is always represented as xyz coordinates, then the submarine detected an enemy battleship, at the following coordinates (6,-3, 6) from the submarine location, the submarine has a torpedo with a maximum range 10KM, so based on the battleship location we need to know the distance and check if this distance within the torpedo range or the submarine has to get closer

We can calculate the distance using the magnitude of the vector using the Pythagorean Theorem which could be used in 3D space too as well by adding Z to the x and y components

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So the torpedo has to travel 9KM which means the battleship is within the effective range.

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