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The magnitude of a vector is its length. The length of a vector is the square root of the sum of each component squared. In this case we have a 2 element vector, but the math extends to 3 element vectors as well by adding the z component (\(\sqrt{x^2+y^2+z^2}\)). In mathematics you'll see the magnitude of a vector represented by absolute value bars (|| or |) surrounding the variable. \[magnitude=\|\textbf{A}\|=\sqrt{A_x^2+A_y^2}\] \[\sqrt{(1)^2+(1)^2}=1.414\] \[=\underline{\underline{1.414}}\]
Note: Calculating the square root is a relatively expensive operation. Many vector libraries offer a squared length method which is faster because it doesn't have to perform a square root. In cases where you don't need the actual length (such as comparing if one vector is longer than another), the squared length is more efficient.