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NDA2020MathematicsThree Dimensional GeometryActual

If a line has direction ratios , then what is the sum of the squares of its direction cosines?

Options

  1. A(a+b+c)^2
  2. B2(a+b+c)
  3. C3
  4. D1

Correct answer

D. 1

Step-by-step solution

Direction ratios are a+b, b+c, c+a Then, direction cosine, aligned & l= (a+b) (a+b)^2+(b+c)^2+(c+a)^2 & m= (b+c) (a+b)^2+(b+c)^2+(c+a)^2 aligned n= (c+a) (a+b)^2+(b+c)^2+(c+a)^2 Sum of squares of direction cosines l^2+m^2+n^2= (a+b)^2+(b+c)^2+(c+a)^2 (a+b)^2+(b+c)^2+(c+a)^2 =1

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