Let a → = − 5 i ^ + j ^ − 3 k ^ , b → = i ^ + 2 j ^ − 4 k ^ and c → = a → × b → × i ^ × i ^ × i ^ . Then c → ⋅ − i ^ + j ^ + k ^ is equal to

Step-by-step solution

Given: a → = − 5 i ^ + j − 3 k ^ and b → = i ^ + 2 j ^ − 4 k ^ ⇒ a → × b → × i ^ = a → ⋅ i ^ b → − b → ⋅ i ^ a → ⇒ a → × b → × i ^ = − 5 b → − a → ⇒ a → × b → × i ^ = − 5 b → − a → × i ^ × i ^ ⇒ a → × b → × i ^ = − 11 j ^ + 23 k ^ × i ^ × i ^ ⇒ a → × b → × i ^ = 11 k ^ + 23 j ^ × i ^ ⇒ a → × b → × i ^ = 11 j ^ − 23 k ^ ⇒ c → . − i ^ + j ^ + k ^ = 11 − 23 ⇒ c → . − i ^ + j ^ + k ^ = − 12