Find the magnitude of the 3D vector v = 3i - 4j + 12k.
Answer and explanation
Correct answer: D. 13
- Step 1: The magnitude of vector v = (x, y, z) is given by ||v|| = sqrt(x^2 + y^2 + z^2).
- Step 2: ||v|| = sqrt(3^2 + (-4)^2 + 12^2) = sqrt(9 + 16 + 144) = sqrt(169) = 13.
Answer
13.
Why not the others: '11' adds the coefficients directly (3 - 4 + 12); '17' adds absolute values (3 + 4 + 12 = 19 - 2); '169' forgets to take the square root.
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