New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

3D Geometry question

2025 · 2 Apr · Shift 1 · Q27

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

PYQ Library
JEE Main
Mathematics
3D Geometry
2025 · 2 Apr · Shift 1 · Q27

3D Geometry question

2025 · 2 Apr · Shift 1 · Q27

JEE MainMathematics3D GeometryMCQ+4 / −1

Let the vertices Q and R of the triangle PQR lie on the line

\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}, \mathrm{QR}=5

and the coordinates of the point

P

be

(0,2,3)

. If the area of the triangle

P Q R

is

\frac{m}{n}

then :

A
$2 \mathrm{~m}-5 \sqrt{21} \mathrm{n}=0$
B
$\mathrm{m}-5 \sqrt{21} \mathrm{n}=0$
C
$5 \mathrm{~m}-21 \sqrt{2} \mathrm{n}=0$
D
$5 \mathrm{~m}-2 \sqrt{21} \mathrm{n}=0$

More from 3D Geometry

Let $A B C D$ be a tetrahedron such that the edges $A D$ and $A D$ are mutually perpendicular. Let the areas of the triangles $ABC, ACD$ and ADB be 5,6 and 7 square units respectively. Then the area (in square units)…2025 · MCQ
If the image of the point $P (1, 0, 3)$ in the line joining the points $A (4, 7, 1)$ and $B (3, 5, 3)$ is $Q (α, β, γ)$ , then $α + β + γ$ is equal to :2025 · MCQ
The line $L_{1}$ is parallel to the vector $a = - 3 \hat{i} + 2 \hat{j} + 4 \hat{k}$ and passes through the point $(7, 6, 2)$ and the line $L_{2}$ is parallel to the vector $b = 2 \hat{i} + \hat{j} + 3 \hat{k}$ …2025 · MCQ
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