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JEE Advanced Mathematics question

MathematicsVector AlgebraJEE Advanced

If are any three vectors such that then is

Answer: (A)

Solution

Adding and subtracting the two conditions: and . By the vector triple product expansion

(Missing argument for \vec\vec a×Missing argument for \vec\vec b)×Missing argument for \vec\vec c = (Missing argument for \vec\vec a·Missing argument for \vec\vec c) Missing argument for \vec\vec b - (Missing argument for \vec\vec b·Missing argument for \vec\vec c) Missing argument for \vec\vec a = 0·Missing argument for \vec\vec b - 0·Missing argument for \vec\vec a = Missing argument for \vec\vec 0.

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Question ID VK-109644