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MCQMediumJEE Main 2026 · 21 January, Shift 1Equation of Line in 3D

Mathematics Question from JEE Main 2026 · 21 January, Shift 1

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:

  • A

    33

  • B

    157\frac{15}{7}

  • C

    187\frac{18}{7}

  • D

    44

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