WEBVTT
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The vector 𝐯 is shown on the grid of units squares below.
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Find the value of the magnitude of 𝐯.
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We know that the magnitude of any vector is its length.
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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.
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The magnitude of vector 𝐯 can therefore be found using Pythagoras’s theorem.
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This states that the length of the hypotenuse is equal to the sum of the squares of the two shorter sides.
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The magnitude of 𝐯 is therefore equal to the square root of 𝑎 squared plus 𝑏 squared.
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Whilst it doesn’t matter which order we substitute the four and the three, we usually do the horizontal component first.
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Four squared is equal to 16, and three squared is equal to nine.
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The magnitude of vector 𝐯 is equal to the square root of 25.
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As 25 is a square number, we can calculate this.
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The square root of 25 is equal to positive or negative five.
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As we’re dealing with a length, our answer must be positive.
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Therefore, the magnitude of vector 𝐯 on the grid is five.