JEE Mains · Maths · STD 12 - 11. three dimension geometry
If the shortest distance between the lines \(\frac{x-\lambda}{-2}=\frac{y-2}{1}=\frac{z-1}{1}\) and \(\frac{x-\sqrt{3}}{1}=\frac{y-1}{-2}=\frac{z-2}{1}\) is \(1 ,\) then the sum of all possible values of \(\lambda\) is :
- A \(0\)
- B \(2 \sqrt{3}\)
- C \(3 \sqrt{3}\)
- D \(-2 \sqrt{3}\)
Answer & Solution
Correct Answer
(B) \(2 \sqrt{3}\)
Step-by-step Solution
Detailed explanation
Passing points of lines \(\mathrm{L}_1 \& \mathrm{~L}_2\) are \((\lambda, 2,1) \&(\sqrt{3}, 1,2)\) \((\lambda, 2,1) \&(\sqrt{3}, 1,2)\) \(S.D\)…
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
- The area of the region enclosed by the parabola \(y=4 x-x^2\) and \(3 y=(x-4)^2\) is equal toJEE Mains 2024 Medium
- In a class of \(60\) students, \(40\) opted for \(NCC,\,30\) opted for \(NSS\) and \(20\) opted for both \(NCC\) and \(NSS.\) If one of these students is selected at random, then the probability that the student selected has opted neither for \(NCC\) nor for \(NSS\) isJEE Mains 2019 Hard
- If \(a _{1}, a _{2}, a _{3} \ldots\) and \(b _{1}, b _{2}, b _{3} \ldots\) are \(A.P.\) and \(a_{1}=2, a_{10}=3, a_{1} b_{1}=1=a_{10} b_{10}\) then \(a_{4} b_{4}\) is equal toJEE Mains 2022 Medium
- \(\lim _{x \rightarrow 0}\left(\frac{(x+2 \cos x)^{3}+2(x+2 \cos x)^{2}+3 \sin (x+2 \cos x)}{(x+2)^{3}+2(x+2)^{2}+3 \sin (x+2)}\right)^{\frac{100}{x}}\)is equal to\(.....\)JEE Mains 2022 Hard
- The area of the region (in sq. units), in the first quadrant bounded by the parabola \(y = 9x^2\) and the lines \(x = 0,y = 1\) and \(y = 4,\) isJEE Mains 2013 Hard
- If the system of equations
\(\begin{aligned}
& 2 x-y+z=4 \\
& 5 x+\lambda y+3 z=12 \\
& 100 x-47 y+\mu z=212
\end{aligned}\)
has infinitely many solutions, then \(\mu-2 \lambda\) is equal toJEE Mains 2025 Easy
More PYQs from JEE Mains
- The number of non-empty equivalence relations on the set \(\{1,2,3\}\) is :JEE Mains 2025 Easy
- Let \(A = \left\{ {0 \in \left( { - \frac{\pi }{2},\pi } \right):\frac{{3 + 2i\,\sin \,\theta }}{{1 - 2i\,\sin \,\theta }}\,{\rm{purely \,imaginary}}} \right\}\). Then the sum of the elements in \(A\) isJEE Mains 2019 Hard
- If the first term of an \(A.P.\) is \(3\) and the sum of its first \(25\) terms is equal to the sum of its next \(15\) terms, then the common difference of this \(A.P.\) is :JEE Mains 2020 Hard
- Let \(f\) be a twice differentiable function on \(R\). If \(f^{\prime}(0)=4\) and \(f(x)+\int_{0}^{x}(x-t) f^{\prime}(t) d t=\left(e^{2 x}+e^{-2 x}\right) \cos 2 x+\frac{2}{a} x\) then \((2 a+1)^{5} a^{2}\) is equal to \(\dots\dots\)JEE Mains 2022 Hard
- Let \(\alpha|\mathrm{x}|=|\mathrm{y}| \mathrm{e}^{\mathrm{xy}-\beta}, \alpha, \beta \in \mathrm{N}\) be the solution of the differential equation \(x d y-y d x+x y(x d y+y d x)=0\), \(y(1)=2\). Then \(\alpha+\beta\) is equal to ...........JEE Mains 2024 Hard
- Let the point \((p, p+1)\) lie inside the region \(E=\left\{(x, y): 3-x \leq y \leq \sqrt{9-x^2}, 0 \leq x \leq 3\right\}\) If the set of all values of \(p\) is the interval \((a, b)\). then \(b^2+b-a^2\) is equal to \(.................\).JEE Mains 2023 Hard