New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

3D Geometry question

2024 · 27 Jan · Shift 2 · Q53

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

PYQ Library
JEE Main
Mathematics
3D Geometry
2024 · 27 Jan · Shift 2 · Q53

3D Geometry question

2024 · 27 Jan · Shift 2 · Q53

JEE MainMathematics3D GeometryNumerical+4 / −1

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

\mathrm{P}

from the line

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

is

l

, then

14 l^2

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

More from 3D Geometry

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
Let $P (3, 2, 3), Q (4, 6, 2)$ and $R (7, 3, 2)$ be the vertices of $△ PQR$ . Then, the angle $∠ QPR$ is2024 · MCQ
Let O be the origin, and M and $N$ be the points on the lines $\frac{x - 5}{4} = \frac{y - 4}{1} = \frac{z - 5}{3}$ and $\frac{x + 8}{12} = \frac{y + 2}{5} = \frac{z + 11}{9}$ respectively such that $MN$ is the shortest distance between the…2024 · Numerical
Let $(α, β, γ)$ be the foot of perpendicular from the point $(1, 2, 3)$ on the line $\frac{x + 3}{5} = \frac{y - 1}{2} = \frac{z + 4}{3}$ . Then $19 (α + β + γ)$ is equal to :2024 · MCQ
Let $A (2, 3, 5)$ and $C (- 3, 4, - 2)$ be opposite vertices of a parallelogram $A B C D$ . If the diagonal $BD = \hat{i} + 2 \hat{j} + 3 \hat{k}$ , then the area of the parallelogram is equal to :2024 · MCQ
If $d_{1}$ is the shortest distance between the lines $x + 1 = 2 y = - 12 z, x = y + 2 = 6 z - 6$ and $d_{2}$ is the shortest distance between the lines $\frac{x - 1}{2} = \frac{y + 8}{- 7} = \frac{z - 4}{5}, \frac{x - 1}{2} = \frac{y - 2}{1} = \frac{z - 6}{- 3}$ …2024 · Numerical