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JEE Main202331 Jan 2023Evening ShiftMathematicsVector AlgebraActual

Let a → , b → , c → be three vectors such that a → = 31 , 4 b → = c → = 2 and 2 a → × b → = 3 c → × a → . If the angle between b → and c → is 2 π 3 , then a → × c → a → · b → 2 is equal to _____ .

Correct answer

0

Step-by-step solution

Given, a → = 31 ,   4 b → = c → = 2 , 2 a → × b → = 3 c → × a → and angle between b →   &   c → is given as 2 π 3 Now solving, 3 c → × a → + 2 b → × a → = 0 ⇒ 3 c → × 2 b → × a → = 0 Means 3 c → × 2 b →   &   a → are parallel vector, So, let 3 c → × 2 b → = λ a → Now squaring both sides we get, 9 c

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