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MHT CET202615 April 2026Morning ShiftMathematicsThree Dimensional GeometryActual

If a unit vector makes angles 4 with i , 3 with j and (0, ) with k , then a value of is equal to...

Options

  1. A3 , 2 3
  2. B6 , 5 6
  3. C4 , 5 4
  4. D5 12 , 7 12

Correct answer

A. 3 , 2 3

Step-by-step solution

Let the unit vector be a = i + j + k . Given = 4 , = 3 , and = . Using the property of direction cosines, ^2 + ^2 + ^2 = 1 . Substituting the given values: ^2 ( 4 ) + ^2 ( 3 ) + ^2 = 1 ( 1 2 )^2 + ( 1 2 )^2 + ^2 = 1 1 2 + 1 4 + ^2 = 1 3 4 + ^2 = 1 ^2 = 1 4 = 1 2 Since (0, ) , we get = 3 or = 2 3 . Answer: 3 , 2 3

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