Video: The Magnitude of a Vector

The vector 𝐯 is shown on the grid of units squares below. Find the value of |𝐯|.

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Video Transcript

The vector 𝐯 is shown on the grid of units squares below. Find the value of the magnitude of 𝐯.

We know that the magnitude of any vector is its length. By creating a right triangle on the grid, we can see that the vector has moved four units to the right and three units up. The magnitude of vector 𝐯 can therefore be found using Pythagoras’s theorem. This states that the length of the hypotenuse is equal to the sum of the squares of the two shorter sides. The magnitude of 𝐯 is therefore equal to the square root of 𝑎 squared plus 𝑏 squared.

Whilst it doesn’t matter which order we substitute the four and the three, we usually do the horizontal component first. Four squared is equal to 16, and three squared is equal to nine. The magnitude of vector 𝐯 is equal to the square root of 25. As 25 is a square number, we can calculate this. The square root of 25 is equal to positive or negative five. As we’re dealing with a length, our answer must be positive. Therefore, the magnitude of vector 𝐯 on the grid is five.

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