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3D Geometry question

2025 · 4 Apr · Shift 2 · Q44

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JEE Main
Mathematics
3D Geometry
2025 · 4 Apr · Shift 2 · Q44

3D Geometry question

2025 · 4 Apr · Shift 2 · Q44

JEE MainMathematics3D GeometryMCQ+4 / −1

Let the values of p , for which the shortest distance between the lines

\frac{x+1}{3}=\frac{y}{4}=\frac{z}{5}

and

\overrightarrow{\mathrm{r}}=(\mathrm{p} \hat{i}+2 \hat{j}+\hat{k})+\lambda(2 \hat{i}+3 \hat{j}+4 \hat{k})

is

\frac{1}{\sqrt{6}}

, be

\mathrm{a}, \mathrm{b},(\mathrm{a}\lt \mathrm{b})

. Then the length of the latus rectum of the ellipse

\frac{x^2}{\mathrm{a}^2}+\frac{y^2}{\mathrm{~b}^2}=1

is :

A
$\frac{3}{2}$
B
9
C
18
D
$\frac{2}{3}$

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