Compute |w| for w = (−2, 5, −1).

Compute |w| for w = (−2, 5, −1).

• A. √34
• B. √29
• C. √30
• D. √28

Answer: (C)

Think of the magnitude of a vector as its length in space. For a vector with components (a, b, c), its length is the square root of the sum of the squares: sqrt(a^2 + b^2 + c^2). Here the components are -2, 5, and -1. Squaring gives 4, 25, and 1, which sum to 30. The length is sqrt(30). Since sqrt(30) is one of the given options, that is the correct value. The negative signs don’t matter because squaring removes them.

Think of the magnitude of a vector as its length in space. For a vector with components (a, b, c), its length is the square root of the sum of the squares: sqrt(a^2 + b^2 + c^2). Here the components are -2, 5, and -1. Squaring gives 4, 25, and 1, which sum to 30. The length is sqrt(30). Since sqrt(30) is one of the given options, that is the correct value. The negative signs don’t matter because squaring removes them.