New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

3D Geometry question

2025 · 2 Apr · Shift 2 · Q38

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
3D Geometry
2025 · 2 Apr · Shift 2 · Q38

3D Geometry question

2025 · 2 Apr · Shift 2 · Q38

JEE MainMathematics3D GeometryMCQ+4 / −1

The line

\mathrm{L}_1

is parallel to the vector

\overrightarrow{\mathrm{a}}=-3 \hat{i}+2 \hat{j}+4 \hat{k}

and passes through the point

(7,6,2)

and the line

\mathrm{L}_2

is parallel to the vector

\overrightarrow{\mathrm{b}}=2 \hat{i}+\hat{j}+3 \hat{k}

and passes through the point

(5,3,4)

. The shortest distance between the lines

L_1

and

L_2

is :

A
$\frac{23}{\sqrt{38}}$
B
$\frac{21}{\sqrt{38}}$
C
$\frac{23}{\sqrt{57}}$
D
$\frac{21}{\sqrt{57}}$

More from 3D Geometry

Let a line passing through the point $(4, 1, 0)$ intersect the line $L_{1} : \frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}$ at the point $A (α, β, γ)$ and the line $L_{2} : x - 6 = y = - z + 4$ at the point $B (a, b, c)$ . Then $1 α a 0 β b 1 γ c$ …2025 · MCQ
Line $L_{1}$ passes through the point $(1, 2, 3)$ and is parallel to $z$ -axis. Line $L_{2}$ passes through the point $(λ, 5, 6)$ and is parallel to $y$ -axis. Let for $λ = λ_{1}, λ_{2}, λ_{2} < λ_{1}$ , the shortest…2025 · MCQ
Each of the angles $β$ and $γ$ that a given line makes with the positive $y$ - and $z$ -axes, respectively, is half of the angle that this line makes with the positive $x$ -axes. Then the sum of all possible values of the angle $β$ …2025 · MCQ
The distance of the point $(7, 10, 11)$ from the line $\frac{x - 4}{1} = \frac{y - 4}{0} = \frac{z - 2}{3}$ along the line $\frac{x - 9}{2} = \frac{y - 13}{3} = \frac{z - 17}{6}$ is2025 · MCQ
Let the shortest distance between the lines $\frac{x - 3}{3} = \frac{y - α}{- 1} = \frac{z - 3}{1}$ and $\frac{x + 3}{- 3} = \frac{y + 7}{2} = \frac{z - β}{4}$ be $330$ . Then the positive value of $5 α + β$ is2025 · MCQ
Let $A$ and $B$ be two distinct points on the line $L : \frac{x - 6}{3} = \frac{y - 7}{2} = \frac{z - 7}{- 2}$ . Both $A$ and $B$ are at a distance $217$ from the foot of perpendicular drawn from the point $(1, 2, 3)$ on the line $L$ . If $O$ is…2025 · MCQ
Let A be the point of intersection of the lines $L_{1} : \frac{x - 7}{1} = \frac{y - 5}{0} = \frac{z - 3}{- 1}$ and $L_{2} : \frac{x - 1}{3} = \frac{y + 3}{4} = \frac{z + 7}{5}$ . Let B and C be the points on the lines $L_{1}$ and $L_{2}$ …2025 · MCQ
Let the values of p , for which the shortest distance between the lines $\frac{x + 1}{3} = \frac{y}{4} = \frac{z}{5}$ and $r = (p \hat{i} + 2 \hat{j} + \hat{k}) + λ (2 \hat{i} + 3 \hat{j} + 4 \hat{k})$ is $\frac{1}{6}$ …2025 · MCQ