Let a → and b → be two orthogonal unit vectors and c → is a vector such that c → × b → = a → - c → , then c → is equal to

Step-by-step solution

c → × b → = a → − c → Taking dot product with b → , we get, 0 = a → ⋅ b → − c → ⋅ b → ⇒ c → ⋅ b → = 0 As a → ⋅ b → = 0 … … .. i Taking dot product with c → , we get, 0 = a → ⋅ c → − c → 2 ⇒ a → ⋅ c → = c → 2 … … .. ii Taking dot product with a → , we get, c → b → a → = a → ⋅ a → − a → ⋅ c → ⇒ c → b → a → = 1 − c → 2 … … .. iii Given, c → × b → = a → - c → ⇒ c → × b → 2 = a → − c → 2 ​ ⇒ c → 2 b → 2 = a → 2 + c → 2 − 2 a → ⋅ c → From i & ii , we get, c → 2 = 1 + c → 2 − 2 c → 2 ⇒ c → = 1 2