JEE Main 2026 Mathematics question
If and are two vectors such that || = 2 and || = 3, then the maximum value of 3|3 + 2| + 4|3 − 2| is:
Answer: (C)
Solution
|3a + 2b|² + |3a − 2b|² = 2(36 + 36) = 144. By Cauchy–Schwarz, 3u + 4v ≤ 5√(u² + v²) = 5 × 12 = 60, attained for suitable directions.