Let u = (3, -2, 5) and v = (1, 0, -4). What is the magnitude |v|?

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Multiple Choice

Let u = (3, -2, 5) and v = (1, 0, -4). What is the magnitude |v|?

Explanation:
The magnitude of a vector in three dimensions is its length, found by summing the squares of its components and taking the square root: |v| = sqrt(v1^2 + v2^2 + v3^2). For v = (1, 0, -4), this becomes sqrt(1^2 + 0^2 + (-4)^2) = sqrt(1 + 0 + 16) = sqrt(17). So the magnitude is sqrt(17).

The magnitude of a vector in three dimensions is its length, found by summing the squares of its components and taking the square root: |v| = sqrt(v1^2 + v2^2 + v3^2). For v = (1, 0, -4), this becomes sqrt(1^2 + 0^2 + (-4)^2) = sqrt(1 + 0 + 16) = sqrt(17). So the magnitude is sqrt(17).

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