Video: Determining the Norms of Vectors

Given that |𝐀| = 6, |𝐁| = 3, |𝐂| = 14, and all three vectors are mutually perpendicular, determine |𝐀 + 𝐁 + 𝐂|.

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Video Transcript

Given that the magnitude or modulus of vector 𝐀 is equal to six, the magnitude of vector 𝐁 is equal to three, and the magnitude of vector 𝐂 is equal to 14 and all three vectors are mutually perpendicular, determine the magnitude of 𝐀 plus 𝐁 plus 𝐂.

In this question, we’re given the magnitude of three individual vectors. And we need to calculate the magnitude of the sum of these three vectors. The magnitude of 𝐀 plus 𝐁 plus 𝐂 is equal to the square root of the magnitude of 𝐀 squared plus the magnitude of 𝐁 squared plus the magnitude of 𝐂 squared.

Substituting in our values gives us the square root of six squared plus three squared plus 14 squared. Six squared is equal to 36. Three squared is equal to nine. And 14 squared is equal to 196. The sum of these three values is 241. This means that the magnitude of vector 𝐀 plus vector 𝐁 plus vector 𝐂 is equal to the square root of 241.

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