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JEE Main20204 Sep 2020Evening ShiftMathematicsVector AlgebraActual

If a → = 2 i ^ + j ^ + 2 k ^ , then, the value of i ^ × a → × i ^ 2 + j ^ × a → × j ^ 2 + k ^ × a → × k ^ 2 , is equal to :

Correct answer

0

Step-by-step solution

Let a → = x i ^ + y j ^ + z k ^ , and using vector triple product, we have, i ^ × a → × i ^ = i ^ . i ^ a → - i ^ . a → i ^ = y j ^ + z k ^ Similarly, j ^ × a → × j ^ = x i ^ + z k ^ and k ^ × a → × k ^ = x i ^ + y k ^ Thus, i ^ × a → × i ^ 2 + j ^ × a → × j ^ 2 + k ^ × a → × k ^ 2 = y j ^ + z k ^ 2 + x i ^ + z k ^ 2 + x i ^ + y j ^ 2 = 2 | a → | 2 = 2 ( 9 ) = 18

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