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MHT CET202620 April 2026Evening ShiftMathematicsVector AlgebraActual

If u = i + 2 j - 2 k , v = 2 i + k and w is unit vector then the maximum value of scalar triple product [ u v w ] is

Options

  1. A-3 5
  2. B0
  3. C3 5
  4. D54

Correct answer

C. 3 5

Step-by-step solution

The scalar triple product is given by [ u v w ] = ( u v ) w . First, we find the cross product u v : u v = vmatrix i & j & k 1 & 2 & -2 2 & 0 & 1 vmatrix u v = i (2 - 0) - j (1 - (-4)) + k (0 - 4) u v = 2 i - 5 j - 4 k The magnitude of this vector is: | u v | = 2^2 + (-5)^2 + (-4)^2 = 4 + 25 + 16 = 45 = 3 5 The dot product ( u v ) w is maximized when the unit vector w is in the same direction as u v . Maximum value = | u v | | w | (0^ ) Since | w | = 1 , the maximum value is 3 5 1 1 = 3 5 . Answer: 3 5

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