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If 𝐀 = 2𝐢 + 3𝐣 − 𝐤, find |𝐀|.

If vector 𝐀 is equal to two 𝐢 plus three 𝐣 minus 𝐤, find the magnitude of vector 𝐀.

For any vector written in the form 𝑥𝐢 plus 𝑦𝐣 plus 𝑧𝐤, the magnitude of the vector is equal to the square root of 𝑥 squared plus 𝑦 squared plus 𝑧 squared. The 𝐢-component of our vector is equal to two, the 𝐣-component is equal to three, and the 𝐤-component is equal to negative one. This means that the magnitude of vector 𝐀 is equal to the square root of two squared plus three squared plus negative one squared.

Two squared is equal to four. Three squared is equal to nine. Squaring a negative number gives us a positive answer. Therefore, negative one squared is one. As four plus nine plus one equals 14, the magnitude of vector 𝐀 is the square root of 14.

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