JEE Main 2024 Mathematics question
Let a⃗ = 3î + ĵ − 2k̂, b⃗ = 4î + ĵ + 7k̂ and c⃗ = î − 3ĵ + 4k̂ be three vectors. If a vector p⃗ satisfies p⃗ × b⃗ = c⃗ × b⃗ and p⃗·a⃗ = 0, then p⃗·(î − ĵ − k̂) is equal to
Answer: (D)
Solution
(p⃗ − c⃗) × b⃗ = 0, so p⃗ = c⃗ + λb⃗. Then p⃗·a⃗ = 0 gives c⃗·a⃗ + λ b⃗·a⃗ = 0, and c⃗·a⃗ = 3 − 3 − 8 = −8, b⃗·a⃗ = 12 + 1 −
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