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MathsJEE Main 21 Jan 2026, Shift 1·Q14·MCQ·Easy–moderate

3D Geometry · Foot of perpendicular to line

Let (α,β,γ)(\alpha, \beta, \gamma) be the co-ordinates of the foot of the perpendicular drawn from the point (5,4,2)(5, 4, 2) on the line r⃗=(−i^+3j^+k^)+λ(2i^+3j^−k^)\vec r = (-\hat i + 3\hat j + \hat k) + \lambda(2\hat i + 3\hat j - \hat k). Then the length of the projection of the vector αi^+βj^+γk^\alpha\hat i + \beta\hat j + \gamma\hat k on the vector 6i^+2j^+3k^6\hat i + 2\hat j + 3\hat k is:
  1. (1)157\dfrac{15}{7}
  2. (2)4
  3. (3)187\dfrac{18}{7}
  4. (4)3

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