JEE Main 2024 Mathematics question
If λ > 0, let θ be the angle between the vectors and . If the vectors and are mutually perpendicular, then the value of is equal to
Answer: (A)
Solution
(a + b)·(a − b) = 0 gives |a|² = |b|²: 10 + λ² = 14 ⇒ λ = 2. Then a·b = 3 − 2 − 6 = −5 and 14 cos θ = −5, so (14 cos θ)² = 25.