Let a → = 3 i ^ + j ^ − 2 k ^ , b → = 4 i ^ + j ^ + 7 k ^ and c → = i ^ − 3 j ^ + 4 k ^ be three vectors. If a vectors p → satisfies p → × b → = c → × b → and p → ⋅ a → = 0 , then p → ⋅ i ^ − j ^ − k ^ is equal to

Step-by-step solution

Given: p → × b → = c → × b → ⇒ p → - c → × b → = 0 ⇒ p → - c → | | b → ⇒ p → - c → = k b → ⇒ p → = k b → + c → ⇒ p → = 4 k + 1 i ^ + k - 3 j ^ + 7 k + 4 k ^ Now, p → . a → = 0 ⇒ 3 4 k + 1 + k - 3 - 2 7 k + 4 = 0 ⇒ k = - 8 ⇒ p → = - 31 i ^ - 11 j ^ - 52 k ^ ⇒ p → . i ^ - j ^ - k ^ = - 31 + 11 + 52 ⇒ p → . i ^ - j ^ - k ^ = 32