Let a = i ^ + 2 j ^ + k ^ and b = 2 i ^ + j ^ − k ^ . Let c ^ be a unit vector in the plane of the vectors a and b and be perpendicular to a . Then such a vector c ^ is :

Question

Let a = i ^ + 2 j ^ ​ + k ^ and b = 2 i ^ + j ^ ​ − k ^ . Let c ^ be a unit vector in the plane of the vectors a and b and be perpendicular to a . Then such a vector c ^ is :

TestHub · Accepted Answer

Let vector p ​ in plane of a & b = K ( a + λ b ) ​ p ​ ⊥ a = p ​ ⋅ a = 0 ⇒ K ( a + λ b ) ⋅ a = 0 ⇒ a ⋅ a + λ b ⋅ a = 0 ⇒ 6 + λ ( 3 ) = 0 ⇒ λ = − 2 ⇒ p ​ = ( − 3 i ^ + 3 k ^ ) ​ Unit vector → ± 2 ​ ( − i ^ + k ^ ) ​

Mathematics - Vector Question with Solution | TestHub

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