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

BlackTom AI · Accepted Answer

The question asks which function would determine the length (or norm) of a vector v. 
Option 1: 'log(v)'. This is incorrect because the logarithm of a vector is not a standard length measure; log is defined for scalar positive values and does not yield a vector norm.
Option 2: 'sqrt(sum(v^2))'. This expression computes the square root of the sum of the squared components of v, which is the Euclidean norm (L2 norm) of the vector in R^n. It directly corresponds to the standard length of v.
Option 3: 'norm(v)'. In many programming languages and mathematical contexts, 'norm(v)' denotes a vector norm, which could refer to various norms (L1, L2, etc.) depending on context. Without specification, it is ambiguous, though commonly norm(v) can mean the Euclidean norm as well. However, since the explicit form sqrt(sum(v^2)) is provided and matches the standard Euclidean length, this option could be considered equivalent in contexts where norm defaults to the L2 norm, but the question asks for a function to determine the length; using the explicit expression is the direct method.
Option 4: 'length(v)'. This is not a universal mathematical function for vector norms; in many programming languages, length(v) refers to the number of elements in the vector rather than its magnitude, making this incorrect for length as a vector norm.

In summary, the expression that directly computes the Euclidean length of v is sqrt(sum(v^2)); it captures the essential idea of the vector’s magnitude by summing squares and taking the square root. Other options either compute an unrelated quantity (log), rely on ambiguous or context-dependent definitions (norm in some cases), or refer to a count of elements (length) rather than magnitude.

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

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