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

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

• A. √34
• B. √40
• C. √38
• D. √42

Answer: (C)

The length of a three-dimensional vector comes from the square-root of the sum of the squares of its components. For u = (3, -2, 5), compute 3^2 + (-2)^2 + 5^2 = 9 + 4 + 25 = 38, so |u| = sqrt(38). The other options would require the sum of squares to be 34, 40, or 42, which doesn’t match the actual squares 9, 4, and 25 for this vector.

The length of a three-dimensional vector comes from the square-root of the sum of the squares of its components. For u = (3, -2, 5), compute 3^2 + (-2)^2 + 5^2 = 9 + 4 + 25 = 38, so |u| = sqrt(38). The other options would require the sum of squares to be 34, 40, or 42, which doesn’t match the actual squares 9, 4, and 25 for this vector.