New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

3D Geometry question

2023 · 6 Apr · Shift 2 · Q42

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

PYQ Library
JEE Main
Mathematics
3D Geometry
2023 · 6 Apr · Shift 2 · Q42

3D Geometry question

2023 · 6 Apr · Shift 2 · Q42

JEE MainMathematics3D GeometryNumerical+4 / −1

If the lines

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

and

\frac{x-4}{5}=\frac{y-1}{2}=\frac{z}{\beta}

intersect, then the magnitude of the minimum value of

8 \alpha \beta

is

\underline{\hspace{2cm}}

.

Numerical answer

More from 3D Geometry

The shortest distance between the lines $\frac{x - 4}{4} = \frac{y + 2}{5} = \frac{z + 3}{3}$ and $\frac{x - 1}{3} = \frac{y - 3}{4} = \frac{z - 4}{2}$ is :2023 · MCQ
The shortest distance between the lines $\frac{x + 2}{1} = \frac{y}{- 2} = \frac{z - 5}{2}$ and $\frac{x - 4}{1} = \frac{y - 1}{2} = \frac{z + 3}{0}$ is :2023 · MCQ
Let a line $l$ pass through the origin and be perpendicular to the lines $l_{1} : r = (\overset{}{^} - 11 \overset{}{^} - 7 \hat{k}) + λ (\hat{i} + 2 \overset{}{^} + 3 \hat{k}), λ \in R$ and $l_{2} : r = (- \overset{}{^} + \hat{k}) + μ (2 \overset{}{^} + 2 \overset{}{^} + \hat{k}), μ \in R$ …2023 · Numerical
Let the lines $l_{1} : \frac{x + 5}{3} = \frac{y + 4}{1} = \frac{z - α}{- 2}$ and $l_{2} : 3 x + 2 y + z - 2 = 0 = x - 3 y + 2 z - 13$ be coplanar. If the point $P (a, b, c)$ on $l_{1}$ is nearest to the point $Q (- 4, - 3, 2)$ , then $∣ a ∣ + ∣ b ∣ + ∣ c ∣$ …2023 · MCQ
The line, that is coplanar to the line $\frac{x + 3}{- 3} = \frac{y - 1}{1} = \frac{z - 5}{5}$ , is :2023 · MCQ
Let $S$ be the set of all values of $λ$ , for which the shortest distance between the lines $\frac{x - λ}{0} = \frac{y - 3}{4} = \frac{z + 6}{1}$ and $\frac{x + λ}{3} = \frac{y}{- 4} = \frac{z - 6}{0}$ is 13. Then $8 λ \in S \sum λ$ …2023 · MCQ
The shortest distance between the lines $\frac{x - 2}{3} = \frac{y + 1}{2} = \frac{z - 6}{2}$ and $\frac{x - 6}{3} = \frac{1 - y}{2} = \frac{z + 8}{0}$ is equal to 2023 · Numerical
If the shortest between the lines $\frac{x + 6}{2} = \frac{y - 6}{3} = \frac{z - 6}{4}$ and $\frac{x - λ}{3} = \frac{y - 2 6}{4} = \frac{z + 2 6}{5}$ is 6, then the square of sum of…2023 · Numerical