Let a → = 3 i ^ + 2 j ^ + 2 k ^ and b → = i ^ + 2 j ^ - 2 k ^ be two vectors. If a vector…

Let a→=3i^+2j^+2k^ and b→=i^+2j^-2k^ be two vectors. If a vector perpendicular to both the vectors a→+b→ and a→-b→  has the magnitude 12 then one such vector is:
  1. 4(2i^+2j^+k^)
  2. 4(2i^-2j^-k^)
  3. 4(-2i^-2j^+k^)
  4. 4(2i^+2j^-k^)

Solution

a→=3i^+2j^+2k^,b→=i+2j^-2k^
∵ α→=a→+b→=4i^+4j^
 β→=a→-b→=2i^+4k^
∴ α→×β→=i^j^k^440204=i^16-j^16+k^-8=16i^-16j^-8k^
∴ Unit vector perpendicular to  α→& β→ is
n^=α→×β→α→×β→=2i^-2j^-k^3
∴ Required vector =122i^-2j^-k^3=42i^-2j^-k^

Asked in: JEE Main 2019 (12 Apr Shift 1)

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