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JEE Main202311 Apr 2023Evening ShiftMathematicsVector AlgebraActual

Let a → = i ^ + 2 j ^ + 3 k ^ and b → = i ^ + j ^ - k ^ . If c → is a vector such that a → · c → = 11 , b → · a → × c → = 27 and b → · c → = - 3 | b → | , then | a → × c → | 2 is equal to

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Step-by-step solution

Given, a → = i ^ + 2 j ^ + 3 k ^ , b → = i ^ + j ^ - k ^ , a → · c → = 11 , b → · a → × c → = 27 and b → · c → = - 3 b → Now finding, b → × a → we get, b → × a → = i ^ j ^ k ^ 1 1 - 1 1 2 3 = 5 i ^ - 4 j ^ + k ^ Let c → = c 1 i ^ + c 2 j ^ + c 3 k ^ Now solving, a → · c → = 11 we get, c 1 + 2 c 2 + 3 c 3 = 11   . . . . . . . 1 Now solving, b → · c → = - 3 b &

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