Question at position 6 Which function would you use to determine the length (or norm) of a vector v?norm(v)sqrt(sum(v^2))log(v)length(v)

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Question at position 6 Which function would you use to determine the length (or norm) of a vector v?norm(v)sqrt(sum(v^2))log(v)length(v)

BlackTom AI · Accepted Answer

To tackle this question about vector length, we need to identify which option corresponds to the mathematical concept of the vector’s length, also known as its norm.
Option 1: norm(v) — This is the standard function name used in many mathematical and programming contexts to compute the vector’s length (the norm). It directly expresses the intended operation, making it the correct choice in this context.
Option 2: sqrt(sum(v^2)) — This expression is mathematically equivalent to the length of v in Euclidean space: it computes the square root of the sum of squares of the components. While it yields the same value as the norm, it is not a named function by itself but rather a formula. Depending on interpretation, it represents the same concept, but it’s not the function name.
Option 3: log(v) — This option applies a logarithm to the vector, which is not a standard operation for measuring vector length and does not relate to the magnitude or norm. It’s conceptually inappropriate for this purpose.
Option 4: length(v) — Some libraries or languages use length(v) to describe magnitude, but this is language- or context-specific and not as universally correct as norm(v). In many rigorous mathematical texts, norm(v) is the preferred term, and length(v) may be undefined or refer to a different quantity in certain frameworks.
Overall, the reasoning hinges on recognizing that norm(v) is the conventional, named function for the vector’s length, while the other options either express the same idea in formula form, apply an unrelated operation, or depend on specific language conventions.

Question at position 6 Which function would you use to determine the length (or norm) of a vector v?norm(v)sqrt(sum(v^2))log(v)length(v)

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