JEE Mains · Maths · STD 12 - 11. three dimension geometry
The shortest distance between the lines \(\dfrac{x-4}{1} = \dfrac{y-3}{2} = \dfrac{z-2}{-3}\) and \(\dfrac{x+2}{2} = \dfrac{y-6}{4} = \dfrac{z-5}{-5}\) is :
- A \(\dfrac{5\sqrt{6}}{6}\)
- B \(2\sqrt{5}\)
- C \(3\sqrt{5}\)
- D \(4\sqrt{5}\)
Answer & Solution
Correct Answer
(C) \(3\sqrt{5}\)
Step-by-step Solution
Detailed explanation
The given lines are \(L_1: \dfrac{x-4}{1} = \dfrac{y-3}{2} = \dfrac{z-2}{-3}\) and \(L_2: \dfrac{x+2}{2} = \dfrac{y-6}{4} = \dfrac{z-5}{-5}\). For \(L_1\), a point on the line is \(\vec{a}_1 = 4\hat{i} + 3\hat{j} + 2\hat{k}\) and its direction vector is…
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
- A ray of light along \(x + \sqrt 3 y = \sqrt 3 \) gets reflected upon reaching \(x- \) axis , the equation of the reflected ray isJEE Mains 2013 Hard
- If \(\mathrm{x}=2 \sin \theta-\sin 2 \theta\) and \(\mathrm{y}=2 \cos \theta-\cos 2 \theta\) ; \(\theta \in[0,2 \pi],\) then \(\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}\) at \(\theta=\pi\) is :JEE Mains 2020 Hard
- 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 m and \(\mathrm{n},(\mathrm{m} \lt \mathrm{n})\) be two 2-digit numbers. Then the total numbers of pairs \((m, n)\), such that \(\operatorname{gcd}(m, n)=6\), is ________JEE Mains 2025 Hard
- Let \(y^2=12 x\) be the parabola and \(S\) be its focus. Let PQ be a focal chord of the parabola such that \((\mathrm{SP})(\mathrm{SQ})=\frac{147}{4}\). Let C be the circle described taking PQ as a diameter. If the equation of a circle \(C\) is \(64 x^2+64 y^2-\alpha x-64 \sqrt{3} y=\beta\), then \(\beta-\alpha\) is equal to ________.JEE Mains 2025 Hard
- The sum of all values of \(\alpha\), for which the points whose position vectors \(\hat{i}-2 \hat{j}+3 \hat{k}, 2 \hat{i}-3 \hat{j}+4 \hat{k}\), \((\alpha+1) \hat{i}+2 \hat{k}\) and \(9 \hat{i}+(\alpha-8) \hat{j}+6 \hat{k}\) are coplanar, is equal toJEE Mains 2023 Medium
More PYQs from JEE Mains
- If the coefficients of \(x\) and \(x^2\) in \((1+x)^p(1-x)^q\) are \(4\) and \(-5\) respectively, then \(2 p+3 q\) is equal toJEE Mains 2023 Hard
- If \(P = \left[ {\begin{array}{*{20}{c}}
{\frac{{\sqrt 3 }}{2}}&{\frac{1}{2}}\\
{ - \frac{1}{2}}&{\frac{{\sqrt 3 }}{2}}
\end{array}} \right],\,A = \,\left[ {\begin{array}{*{20}{c}}
1&1\\
0&1
\end{array}} \right]\) and \(Q=PAP^T,\) then \(P^T\) \(Q^{2015}\) \(P\) isJEE Mains 2016 Medium - If a variable line, \(3x + 4y -\lambda = 0\) is such that the two circles \(x^2 + y^2 -2x -2y + 1 = 0\) and \(x^2 + y^2 -18x -2y + 78 = 0\) are on its opposite sides, then the set of all values of \(\lambda \) is the intervalJEE Mains 2019 Hard
- \(S = {\tan ^{ - 1}}\left( {\frac{1}{{{n^2} + n + 1}}} \right) + {\tan ^{ - 1}}\left( {\frac{1}{{{n^2} + 3n + 3}}} \right) + ..... + {\tan ^{ - 1}}\left( {\frac{1}{{1 + \left( {n + 19} \right)\left( {n + 20} \right)}}} \right)\) , then \(tan\,S\) is equal toJEE Mains 2013 Hard
- If the tangent to the curve, \(y = x^3 + ax -b\) at the point \((1, -5)\) is perpendicular to the line, \(-\,x + y + 4 = 0,\) then which one of the following, points lies on the curveJEE Mains 2019 Hard
- If \(f(x)=\left\{\begin{array}{ll}{\frac{\sin (a+2) x+\sin x}{x}} & {; x<0} \\ {b} & {; x=0} \\ {\frac{\left(x+3 x^{2}\right)^{\frac{1}{3}}-x^{\frac{1}{3}}}{x^{\frac{4}{3}}}} & {; x>0}\end{array}\right.\) is continuous at \(x=0,\) then \(a+2 b\) is equal toJEE Mains 2020 Hard