JEE Main 2024 Mathematics question
Let a⃗ = 3î + 2ĵ + k̂, b⃗ = 2î − ĵ + 3k̂ and c⃗ be a vector such that (a⃗ + b⃗) × c⃗ = 2(a⃗ × b⃗) + 24ĵ − 6k̂ and (a⃗ − b⃗ + î)·c⃗ = −3. then |c⃗|² is equal to .
Answer: 38
Solution
a⃗ + b⃗ = 5î + ĵ + 4k̂ and a⃗ × b⃗ = 7î − 7ĵ − 7k̂, so the right-hand side is 14î + 10ĵ − 20k̂. With c⃗ = xî + yĵ + zk̂: (a⃗ + b⃗) × c⃗ = (z − 4y)î − (5z − 4x)ĵ + (5y − x)k̂, which
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