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If i ^ × a → - j ^ × i ^ + j ^ × a → - k ^ × j ^ + k ^ × a → - i ^ × k ^ = 0 and a → = x i ^ + y j ^ + z k ^ , then the value of 8 x 3 - x y + z x is equal to

Correct answer

1

Step-by-step solution

i ^ × a → - j ^ × i ^ = i ^ . i ^ a → - j ^ - i ^ . a → - j ^ i ^ = a → - j ^ - i ^ . a → i ^ Therefore, a → - j ^ - i ^ . a → i ^ + a → - k ^ + j ^ . a → j ^ + a → - i ^ - k ^ . a → k ^ = 0 ⇒ 3 a → - i ^ + j ^ + k ^ - a → = 0 a → = 1 2 i ^ + j ^ + k ^ = x i ^ + y j ^ + z k ^ x = y = z = 1 2 8 x 3 - x y + z x = 8 x 3 - x 2 + x 2 = 8 × 1 8 = 1

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