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:

Step-by-step solution

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 ^