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JEE Main2009MathematicsThree Dimensional GeometryActual

The projections of a vector on the three coordinate axis are 6,-3,2 respectively. The direction cosines of the vector are

Options

  1. A6,-3,2
  2. B6 5 ,- 3 5 , 2 5
  3. C6 7 ,- 3 7 , 2 7
  4. D- 6 7 ,- 3 7 , 2 7

Correct answer

C. 6 7 ,- 3 7 , 2 7

Step-by-step solution

Projection of a vector on coordinate axis are x₂-x₁, y₂-y₁, z₂-z₁ aligned & x₂-x₁=6, y₂-y₁=-3, z₂-z₁=2 & (x₂-x₁ )^2+ (y₂-y₁ )^2+ (z₂-z₁ )^2 = 36+9+4 =7 aligned The D.C's of the vector are 6 7 ,- 3 7 , 2 7

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