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NDA2020MathematicsThree Dimensional GeometryActual

Let A be a point in space such that | O A |=12 , where O is the origin. If O A is inclined at angles 45^ and 60^ with x axis and y -axis respectively, then what is O A equal to ?

Options

  1. A6 i +6 j 2 k
  2. B6 i +6 2 j 6 k
  3. C6 2 i +6 j 6 k
  4. D3 2 i +3 j 6 k

Correct answer

C. 6 2 i +6 j 6 k

Step-by-step solution

Let A=(x, y, z) Then, | O A |= x^2+y^2+z^2 =12 Also, x=| O A | 45^ =12 1 2 =6 2 i . y=|O A| 60^ =12 1 2 =6 j Hence, O A =6 2 i +6 j 6 k

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