New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

3D Geometry question

2024 · 9 Apr · Shift 2 · Q46

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

PYQ Library
JEE Main
Mathematics
3D Geometry
2024 · 9 Apr · Shift 2 · Q46

3D Geometry question

2024 · 9 Apr · Shift 2 · Q46

JEE MainMathematics3D GeometryMCQ+4 / −1

Consider the line

\mathrm{L}

passing through the points

(1,2,3)

and

(2,3,5)

. The distance of the point

\left(\frac{11}{3}, \frac{11}{3}, \frac{19}{3}\right)

from the line

\mathrm{L}

along the line

\frac{3 x-11}{2}=\frac{3 y-11}{1}=\frac{3 z-19}{2}

is equal to

A
6
B
3
C
5
D
4

More from 3D Geometry

The square of the distance of the image of the point $(6, 1, 5)$ in the line $\frac{x - 1}{3} = \frac{y}{2} = \frac{z - 2}{4}$ , from the origin is .2024 · Numerical
The distance, of the point $(7, - 2, 11)$ from the line $\frac{x - 6}{1} = \frac{y - 4}{0} = \frac{z - 8}{3}$ along the line $\frac{x - 5}{2} = \frac{y - 1}{- 3} = \frac{z - 5}{6}$ , is :2024 · MCQ
If the shortest distance between the lines $\frac{x - 4}{1} = \frac{y + 1}{2} = \frac{z}{- 3}$ and $\frac{x - λ}{2} = \frac{y + 1}{4} = \frac{z - 2}{- 5}$ is $\frac{6}{5}$ , then the sum of all possible values of $λ$ is :2024 · MCQ
Let the image of the point $(1, 0, 7)$ in the line $\frac{x}{1} = \frac{y - 1}{2} = \frac{z - 2}{3}$ be the point $(α, β, γ)$ . Then which one of the following points lies on the line passing through $(α, β, γ)$ and making…2024 · MCQ
The lines $\frac{x - 2}{2} = \frac{y}{- 2} = \frac{z - 7}{16}$ and $\frac{x + 3}{4} = \frac{y + 2}{3} = \frac{z + 2}{1}$ intersect at the point $P$ . If the distance of $P$ from the line $\frac{x + 1}{2} = \frac{y - 1}{3} = \frac{z - 1}{1}$ is $l$ , then $14 l^{2}$ …2024 · Numerical
Let $O$ be the origin and the position vectors of $A$ and $B$ be $2 \hat{i} + 2 \hat{j} + \hat{k}$ and $2 \hat{i} + 4 \hat{j} + 4 \hat{k}$ respectively. If the internal bisector of $∠ AOB$ meets the line $AB$ at…2024 · MCQ
Let $P QR$ be a triangle with $R (- 1, 4, 2)$ . Suppose $M (2, 1, 2)$ is the mid point of $PQ$ . The distance of the centroid of $△ PQR$ from the point of intersection of the lines $\frac{x - 2}{0} = \frac{y}{2} = \frac{z + 3}{- 1}$ …2024 · MCQ
A line with direction ratios $2, 1, 2$ meets the lines $x = y + 2 = z$ and $x + 2 = 2 y = 2 z$ respectively at the points $P$ and $Q$ . If the length of the perpendicular from the point $(1, 2, 12)$ to the line $PQ$ is $l$ , then $l^{2}$ …2024 · Numerical