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MCQMediumJEE Main 2024 · 31 January, Shift 1Equation of Line in 3D

Mathematics Question from JEE Main 2024 · 31 January, Shift 1

The distance of the point Q(0,2,−2)Q(0, 2, -2) from the line passing through the point P(5,−4,3)P(5, -4, 3) and perpendicular to the lines r⃗=(−3i⃗+2k⃗)+λ(2i⃗+3j⃗+5k⃗),λ∈R\vec{r} = (-3\vec{i} + 2\vec{k}) + \lambda(2\vec{i} + 3\vec{j} + 5\vec{k}), \lambda \in \mathbb{R} and r⃗=(i⃗−2j⃗+k⃗)+μ(−i⃗+3j⃗+2k⃗),μ∈R\vec{r} = (\vec{i} - 2\vec{j} + \vec{k}) + \mu(-\vec{i} + 3\vec{j} + 2\vec{k}), \mu \in \mathbb{R} is:

  • A

    86\sqrt{86}

  • B

    20\sqrt{20}

  • C

    54\sqrt{54}

  • D

    74\sqrt{74}

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