New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

3D Geometry question

2025 · 24 Jan · Shift 2 · Q46

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

PYQ Library
JEE Main
Mathematics
3D Geometry
2025 · 24 Jan · Shift 2 · Q46

3D Geometry question

2025 · 24 Jan · Shift 2 · Q46

JEE MainMathematics3D GeometryNumerical+4 / −1

Let P be the image of the point

\mathrm{Q}(7,-2,5)

in the line

\mathrm{L}: \frac{x-1}{2}=\frac{y+1}{3}=\frac{z}{4}

and

\mathrm{R}(5, \mathrm{p}, \mathrm{q})

be a point on

L

. Then the square of the area of

\triangle P Q R

is

\underline{\hspace{2cm}}

.

Numerical answer

More from 3D Geometry

Let $A (x, y, z)$ be a point in $x y$ -plane, which is equidistant from three points $(0, 3, 2), (2, 0, 3)$ and $(0, 0, 1)$ . Let $B = (1, 4, - 1)$ and $C = (2, 0, - 2)$ . Then among the statements (S1) : $△ ABC$ is…2025 · MCQ
If the image of the point $(4, 4, 3)$ in the line $\frac{x - 1}{2} = \frac{y - 2}{1} = \frac{z - 1}{3}$ is $(α, β, γ)$ , then $α + β + γ$ is equal to2025 · MCQ
The square of the distance of the point $(\frac{15}{7}, \frac{32}{7}, 7)$ from the line $\frac{x + 1}{3} = \frac{y + 3}{5} = \frac{z + 5}{7}$ in the direction of the vector $\hat{i} + 4 \hat{j} + 7 \hat{k}$ is:2025 · MCQ
Let $L_{1} : \frac{x - 1}{1} = \frac{y - 2}{- 1} = \frac{z - 1}{2}$ and $L_{2} : \frac{x + 1}{- 1} = \frac{y - 2}{2} = \frac{z}{1}$ be two lines. Let $L_{3}$ be a line passing through the point $(α, β, γ)$ and be perpendicular to both $L_{1}$ …2025 · MCQ
Let a straight line $L$ pass through the point $P (2, - 1, 3)$ and be perpendicular to the lines $\frac{x - 1}{2} = \frac{y + 1}{1} = \frac{z - 3}{- 2}$ and $\frac{x - 3}{1} = \frac{y - 2}{3} = \frac{z + 2}{4}$ . If the line $L$ intersects the…2025 · MCQ
Let P be the foot of the perpendicular from the point $(1, 2, 2)$ on the line $L : \frac{x - 1}{1} = \frac{y + 1}{- 1} = \frac{z - 2}{2}$ . Let the line $r = (- \hat{i} + \hat{j} - 2 \hat{k}) + λ (\hat{i} - \hat{j} + \hat{k}), λ \in R$ …2025 · MCQ
If the shortest distance between the lines $\frac{x - λ}{- 2} = \frac{y - 2}{1} = \frac{z - 1}{1}$ and $\frac{x - 3}{1} = \frac{y - 1}{- 2} = \frac{z - 2}{1}$ is 1 , then the sum of all possible values of $λ$ is :2024 · MCQ
Let the line of the shortest distance between the lines $L_{1} : r = (\hat{i} + 2 \hat{j} + 3 \hat{k}) + λ (\hat{i} - \hat{j} + \hat{k}) and L_{2} : r = (4 \hat{i} + 5 \hat{j} + 6 \hat{k}) + μ (\hat{i} + \hat{j} - \hat{k})$ …2024 · Numerical