New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

3D Geometry question

2024 · 29 Jan · Shift 1 · Q47

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

PYQ Library
JEE Main
Mathematics
3D Geometry
2024 · 29 Jan · Shift 1 · Q47

3D Geometry question

2024 · 29 Jan · Shift 1 · Q47

JEE MainMathematics3D GeometryMCQ+4 / −1

Let

P Q R

be a triangle with

R(-1,4,2)

. Suppose

M(2,1,2)

is the mid point of

\mathrm{PQ}

. The distance of the centroid of

\triangle \mathrm{PQR}

from the point of intersection of the lines

\frac{x-2}{0}=\frac{y}{2}=\frac{z+3}{-1}

and

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

is

A
69
B
$\sqrt{99}$
C
$\sqrt{69}$
D
9

More from 3D Geometry

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
Let $L_{1} : r = (\hat{i} - \hat{j} + 2 \hat{k}) + λ (\hat{i} - \hat{j} + 2 \hat{k}), λ \in R$ , $L_{2} : r = (\hat{j} - \hat{k}) + μ (3 \hat{i} + \hat{j} + p \hat{k}), μ \in R, and L_{3} : r = δ (ℓ \hat{i} + m \hat{j} + n \hat{k}), δ \in R$ …2024 · MCQ
Let a line passing through the point $(- 1, 2, 3)$ intersect the lines $L_{1} : \frac{x - 1}{3} = \frac{y - 2}{2} = \frac{z + 1}{- 2}$ at $M (α, β, γ)$ and $L_{2} : \frac{x + 2}{- 3} = \frac{y - 2}{- 2} = \frac{z - 1}{4}$ at $N (a, b, c)$ . Then, the value of $\frac{( α + β + γ ) ^{2}}{( a + b + c ) ^{2}}$ …2024 · Numerical