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MathsJEE Main 23 Jan 2026, Shift 1·Q20·MCQ·Moderate

3D Geometry · Angle between lines from direction cosines

Let the direction cosines of two lines satisfy the equations: 4ℓ+m−n=04\ell + m - n = 0 and 2mn+10nℓ+3ℓm=02mn + 10n\ell + 3\ell m = 0. Then the cosine of the acute angle between these lines is:
  1. (1)1038\dfrac{10}{\sqrt{38}}
  2. (2)20338\dfrac{20}{3\sqrt{38}}
  3. (3)10738\dfrac{10}{7\sqrt{38}}
  4. (4)10338\dfrac{10}{3\sqrt{38}}

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