Let u = 2i + 3j, v = –i, and w = 5i – 6j. What is the magnitude of 2(u – v + w)?

Write the vectors as components: u = (2, 3), v = (−1, 0), and w = (5, −6). Then u − v + w = (2, 3) − (−1, 0) + (5, −6) = (8, −3), so 2(u − v + w) = (16, −6). Its magnitude is √(16² + (−6)²) = √292 ≈ 17.1, so the answer is C, 17.1.

AI-written and checked against the verified answer.