JEE Main 2024 Mathematics question
Let three vectors a⃗ = αî + 4ĵ + 2k̂, b⃗ = 5î + 3ĵ + 4k̂, c⃗ = xî + yĵ + zk̂ form a triangle such that c⃗ = a⃗ − b⃗ and the area of the triangle is 5√6. If α is a positive real number, then |c⃗|² is
Answer: (B)
Solution
c⃗ = a⃗ − b⃗ = (α − 5, 1, −2). The area of the triangle is ½|a⃗ × c⃗| = 5√6, so |a⃗ × c⃗| = 10√6. Here a⃗ × c⃗ = (α, 4, 2) × (α − 5, 1, −2) = (−10, 4α
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