Let a → be a non-zero vector. If x → = i ^ × ( a → × i ^ ) , y → = j ^ × ( a → × j ^ ) - a → and z → = k ^ × ( a → × k ^ ) - a → , then x → y → z → =

Question

Let a → be a non-zero vector. If x → = i ^ × ( a → × i ^ ) , y → = j ^ × ( a → × j ^ ) - a → and z → = k ^ × ( a → × k ^ ) - a → , then x → y → z → =, | a ¯ |, 2 | a ¯ |, 0, 1

MARKS App · Accepted Answer

Given, x → = i ^ × ( a → × i ^ ) , y → = j ^ × ( a → × j ^ ) - a → and z → = k ^ × ( a → × k ^ ) - a → ⇒ x → = i ^ · i ^ a → - i ^ · a → i ^ , y → = j ^ · j ^ a → - j ^ · a → j ^ - a → and z → = k ^ · k ^ a → - k ^ · a → k ^ - a → ⇒ x → = a → - i ^ · a → i ^ , y → = - j ^ · a → j ^ and z → = - k ^ . a → k ^ Let, a → = α i ^ + β j ^ + γ k ^ , then x → = β j ^ + γ k ^ , y → = - β j ^ and z → = - γ k ^ . Now, x → y → z → = x → · y → × z → ⇒ x → y → z → = β j ^ + γ k ^ · - β j ^ × - γ k ^ ⇒ x → y → z → = β j ^ + γ k ^ · β γ i ^ = 0

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