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Find the magnitude of the vector 𝐯 shown on the grid of unit squares below.

Any vector, in this case 𝐯, can be written in terms of its 𝑥- and 𝑦-components. Any vector will have an initial or start point and a terminal or endpoint. To get from the initial point to the terminal point, we move one unit right and two units up. This means that vector 𝐯 is equal to one, two. The magnitude of any vector is denoted by absolute value bars. The magnitude is equal to the length of the line segment and can be calculated by finding the sum of the squares of the 𝑥- and 𝑦-components and then square rooting the answer. In this question, the magnitude of vector 𝐯 is equal to the square root of one squared plus two squared. One squared is equal to one, and two squared is equal to four. This means that the magnitude of vector 𝐯 is equal to the square root of five.

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