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NDA2021MathematicsThree Dimensional GeometryActual

Consider the following statements : 1. A line in space can have infinitely many direction ratios. 2. It is possible for certain line that the sum of the squares of direction cosines can be equal to sum of its direction cosines. Which of the above statements is/are correct?

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

C. Both 1 and 2

Step-by-step solution

There are infinitely many different line present in space with different direction ratios. So, statement 1 is correct 1^2+1^2+1^2=1+1+1 so, line have direction cosines 1,1,1 . Such that sum of the squares of direction cosines can be equal to sum of its direction cosines.

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