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Find the direction cosines of a line which makes an angle with all three the coordinate axes.​
  • a)
    ± 1/√2
  • b)
    1/√3
  • c)
    1/√2
  • d)
    ± 1/√3
Correct answer is option 'D'. Can you explain this answer?

Ref: https://edurev.in/question/476432/Find-the-direction-cosines-of-a-line-which-makes-an-angle-with-all-three-the-coordinate-axes-a-12b-

- Toolbox:

Sum of the squares of the direction cosines is one.


We know sum of the squares of the direction cosines is one.

(ie) cos^2 α + cos^2 β + cos^2 γ = 1

But it is given that α = β = γ

Therefore cos^2 α + cos^2 α + cos^2 α = 1

=> 3cos^2 α = 1

Therefore cos^2 α = 1/3

=> cosα = ±1/√3

Hence the direction cosines are (±1/√3,±1/√3, and ±1/√3)

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