New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

3D Geometry question

2025 · 4 Apr · Shift 2 · Q39

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

PYQ Library
JEE Main
Mathematics
3D Geometry
2025 · 4 Apr · Shift 2 · Q39

3D Geometry question

2025 · 4 Apr · Shift 2 · Q39

JEE MainMathematics3D GeometryMCQ+4 / −1

Let A be the point of intersection of the lines

\mathrm{L}_1: \frac{x-7}{1}=\frac{y-5}{0}=\frac{z-3}{-1}

and

\mathrm{L}_2: \frac{x-1}{3}=\frac{y+3}{4}=\frac{z+7}{5}

. Let B and C be the points on the lines

\mathrm{L}_1

and

\mathrm{L}_2

respectively such that

A B=A C=\sqrt{15}

. Then the square of the area of the triangle

A B C

is :

A
63
B
57
C
60
D
54

More from 3D Geometry

Let the values of p , for which the shortest distance between the lines $\frac{x + 1}{3} = \frac{y}{4} = \frac{z}{5}$ and $r = (p \hat{i} + 2 \hat{j} + \hat{k}) + λ (2 \hat{i} + 3 \hat{j} + 4 \hat{k})$ is $\frac{1}{6}$ …2025 · MCQ
Let the line L pass through $(1, 1, 1)$ and intersect the lines $\frac{x - 1}{2} = \frac{y + 1}{3} = \frac{z - 1}{4}$ and $\frac{x - 3}{1} = \frac{y - 4}{2} = \frac{z}{1}$ . Then, which of the following points lies on the line $L$ ?2025 · MCQ
If the shortest distance between the lines $\frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}$ and $\frac{x}{1} = \frac{y}{α} = \frac{z - 5}{1}$ is $\frac{5}{6}$ , then the sum of all possible values of $α$ is2025 · MCQ
If the equation of the line passing through the point $(0, - \frac{1}{2}, 0)$ and perpendicular to the lines $r = λ (\hat{i} + a \hat{j} + b \hat{k})$ and $r = (\hat{i} - \hat{j} - 6 \hat{k}) + μ (- b \hat{i} + a \hat{j} + 5 \hat{k})$ …2025 · MCQ
Consider the lines L1: x - 1 = y - 2 = z and L2: x - 2 = y = z - 1. Let the feet of the perpendiculars from the point P(5, 1, -3) on the lines L1 and L2 be Q and R respectively. If the area of the triangle PQR is A, then 4A2 is equal to :2025 · MCQ
Let the values of $λ$ for which the shortest distance between the lines $\frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}$ and $\frac{x - λ}{3} = \frac{y - 4}{4} = \frac{z - 5}{5}$ is $\frac{1}{6}$ be $λ_{1}$ and $λ_{2}$ .…2025 · MCQ
Let the area of the triangle formed by the lines $x + 2 = y - 1 = z, \frac{x - 3}{5} = \frac{y}{- 1} = \frac{z - 1}{1}$ and $\frac{x}{- 3} = \frac{y - 3}{3} = \frac{z - 2}{1}$ be $A$ . Then $A^{2}$ is equal to .2025 · Numerical
Let $L_{1} : \frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}$ and $L_{2} : \frac{x - 2}{3} = \frac{y - 4}{4} = \frac{z - 5}{5}$ be two lines. Then which of the following points lies on the line of the shortest distance between $L_{1}$ …2025 · MCQ