enEnglishguગુજરાતી
JEE Mains · Maths · STD 12 - 11. three dimension geometry
Shortest distance between the lines \(\frac{x-1}{2}=\frac{y+8}{-7}=\frac{z-4}{5}\) and \(\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-6}{-3}\) is
- A \(2 \sqrt{3}\)
- B \(4 \sqrt{3}\)
- C \(3 \sqrt{3}\)
- D \(5 \sqrt{3}\)
Answer & Solution
Correct Answer
(B) \(4 \sqrt{3}\)
Step-by-step Solution
Detailed explanation
\(\frac{x-1}{2}=\frac{y+8}{-7}=\frac{z-4}{5} \quad \vec{a}=\hat{i}-8 \hat{j}+4 \hat{k}\) \(\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-6}{-3} \quad \vec{b}=\hat{i}+2 \hat{j}+6 \hat{k}\) \(\vec{p}=2 \hat{i}-7 \hat{j}+5 \hat{k}, \overrightarrow{ q }=2 \hat{i}+\hat{j}-3 \hat{k}\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- In a tournament, a team plays \(10\) matches with probabilities of winning and losing each match as \(\frac{1}{3}\) and \(\frac{2}{3}\) respectively. Let \(x\) be the number of matches that the team wins, and \(y\) be the number of matches that team loses. If the probability \(\mathrm{P}(|\mathrm{x}-\mathrm{y}| \leq 2)\) is \(\mathrm{p}\), then \(3^9 \mathrm{p}\) equals ...........JEE Mains 2024 Hard
- Let \(A\) be the point of intersection of the lines \(3 x+\) \(2 y=14,5 x-y=6\) and \(B\) be the point of intersection of the lines \(4 x+3 y=8,6 x+y=5\) The distance of the point \(P(5,-2)\) from the line \(\mathrm{AB}\) isJEE Mains 2024 Medium
- Three balls are drawn at random from a bag containing \(5\) blue and \(4\) yellow balls. Let the random variables \(\mathrm{X}\) and \(\mathrm{Y}\) respectively denote the number of blue and Yellow balls. If \(\bar{X}\) and \(\bar{Y}\) are the means of \(X\) and \(Y\) respectively, then \(7 \bar{X}+4 \bar{Y}\) is equal to ..........JEE Mains 2024 Hard
- \(A (2,6,2), B (-4,0, \lambda), C (2,3,-1)\) and \(D (4,5,0)\), \(|\lambda| \leq 5\) are the vertices of a quadrilateral \(A B C D\). If its area is \(18\) square units, then \(5-6 \lambda\) is equal to \(.........\).JEE Mains 2023 Hard
- Let \(\vec{a}\) and \(\vec{b}\) be two unit vectors such that the angle between them is \(\frac{\pi}{3}\). If \(\lambda \vec{a}+2 \vec{b}\) and \(3 \vec{a}-\lambda \vec{b}\) are perpendicular to each other, then the number of values of \(\lambda\) in \([-1,3]\) is :JEE Mains 2025 Medium
- If the area of the triangle whose one vertex is at the vertex of the parabola, \({y^2} + 4\,\left( {x - {a^2}} \right) = 0\) and the other two vertices are the points of intersection of the parabola and \(y -\) axis, is \(250\, sq\). units, then a value of \(‘a’\) isJEE Mains 2019 Hard
More PYQs from JEE Mains
- If the sum of the coefficients of all the positive even powers of \(x\) in the binomial expansion of \(\left(2 x^{3}+\frac{3}{x}\right)^{10}\) is \(5^{10}-\beta \cdot 3^{9}\), then \(\beta\) is equal toJEE Mains 2022 Hard
- Let \(\mathrm{ABC}\) be an equilateral triangle. A new triangle is formed by joining the middle points of all sides of the triangle \(\mathrm{ABC}\) and the same process is repeated infinitely many times. If \(\mathrm{P}\) is the sum of perimeters and \(Q\) is be the sum of areas of all the triangles formed in this process, then :JEE Mains 2024 Hard
- The probability distribution of random variable \(\mathrm{X}\) is given by:
Let \(\mathrm{p}=\mathrm{P}(1\,<\mathrm{X}\,<\,4 \mid \mathrm{X}\,<\,3)\). If \(5 \mathrm{p}=\lambda \mathrm{K}\), then \(\lambda\) equal to .... .\(X\) \(1\) \(2\) \(3\) \(4\) \(5\) \(P(X)\) \(K\) \(2K\) \(2K\) \(3K\) \(K\) JEE Mains 2021 Medium - Fifteen football players of a club-team are given \(15\) T-shirts with their names written on the backside. If the players pick up the T-shirts randomly, then the probability that at least \(3\) players pick the correct \(T\)-shirt isJEE Mains 2023 Hard
- The value of \(2 \sin(\frac{\pi}{8}) \sin (\frac{2 \pi}{8}) \sin (\frac{3 \pi}{8}) \sin (\frac{5 \pi}{8}) \sin (\frac{6 \pi}{8}) \sin (\frac{7 \pi}{8})\) is:JEE Mains 2021 Medium
- Let \(y = y(x)\) be the solution of the differential equation \(\frac{{dy}}{{dx}} + y\,\tan \,x = 2x\, + \,{x^2}\,\tan \,x\,,\,x\, \in \,\left( { - \frac{\pi }{2},\frac{\pi }{2}} \right),\) such that \(y(0) = 1.\) ThenJEE Mains 2019 Hard