Let a → = 3 i ^ + 2 j ^ + 2 k ^ and b → = i ^ + 2 j ^ - 2 k ^ 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:

Question

Let a → = 3 i ^ + 2 j ^ + 2 k ^ and b → = i ^ + 2 j ^ - 2 k ^ 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:, 4 ( 2 i ^ + 2 j ^ + k ^ ), 4 ( 2 i ^ - 2 j ^ - k ^ ), 4 ( - 2 i ^ - 2 j ^ + k ^ ), 4 ( 2 i ^ + 2 j ^ - k ^ )

MARKS App · Accepted Answer

a → = 3 i ^ + 2 j ^ + 2 k ^ , b → = i + 2 j ^ - 2 k ^ ∵ α → = a → + b → = 4 i ^ + 4 j ^ β → = a → - b → = 2 i ^ + 4 k ^ ∴ α → × β → = i ^ j ^ k ^ 4 4 0 2 0 4 = i ^ 16 - j ^ 16 + k ^ - 8 = 16 i ^ - 16 j ^ - 8 k ^ ∴ Unit vector perpendicular to α → & β → is n ^ = α → × β → α → × β → = 2 i ^ - 2 j ^ - k ^ 3 ∴ Required vector = 12 2 i ^ - 2 j ^ - k ^ 3 = 4 2 i ^ - 2 j ^ - k ^

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