JEE Mains · Maths · STD 12 - 11. three dimension geometry
The plane through the intersection of the plane \(x + y + z = 1\) and \(2x + 3y + z - 4 = 0\) and parallel to \(y -\) axis also pass through the point
- A \((-3, 0, -1)\)
- B \((-3, 1, 1)\)
- C \((3, 3, -1)\)
- D \((3, 2, 1)\)
Answer & Solution
Correct Answer
(D) \((3, 2, 1)\)
Step-by-step Solution
Detailed explanation
Equation of required plane is \((x+y+z-1)+\lambda(2 x+3 y-z+4)=0\) \(\Rightarrow(1+2 \lambda) x+(1+3 \lambda) y+(1-\lambda)=0\) since given plane is parallel to \(y-\) axis \(\Rightarrow 3 \lambda+1=0 \Rightarrow=-\frac{1}{3}\) Hence equation of plane is \(x+4 z-7=0\)
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
- Consider the function : \(f\left( x \right) = \left[ x \right] + \left| {1 - x} \right|,\, - 1 \le x \le 3\) where \([x]\) is the greatest integer function Statement \(1\) :\(f\) is not continuous at \(x = 0, 1, 2\) and \(3\) Statement \(2\) :\(f\left( x \right) = \left( \begin{array}{l}
- x,\,\,\,\,\,\,\,\,\, - 1 \le x < 0\\
1 - x,\,\,\,\,\,\,\,0 \le x < 1\\
1 + x,\,\,\,\,\,\,\,1 \le x < 2\,\\
2 + x,\,\,\,\,\,\,2 \le x \le 3
\end{array} \right.\)JEE Mains 2013 Hard - If the locus of the point, whose distances from the point \((2,1)\) and \((1,3)\) are in the ratio \(5: 4\), is \(a x^2+b y^2+c x y+d x+e y+170=0\), then the value of \(\mathrm{a}^2+2 \mathrm{~b}+3 \mathrm{c}+4 \mathrm{~d}+\mathrm{e}\) is equal to :JEE Mains 2024 Hard
- The number of ways in which \(21\) identical apples can be distributed among three children such that each child gets at least \(2\) apples, isJEE Mains 2024 Medium
- If \(A\, = \,\left[ {\begin{array}{*{20}{c}}
1&2&x\\
3&{ - 1}&2
\end{array}} \right]\) and \(B\, = \,\left[ {\begin{array}{*{20}{c}}
y\\
x\\
1
\end{array}} \right]\) be such that \(AB\, = \,\left[ {\begin{array}{*{20}{c}}
6\\
8
\end{array}} \right],\) thenJEE Mains 2014 Hard - If \(\mathop {\lim }\limits_{n \to \infty } \frac{{{1^a} + {2^a} + ....... + {n^a}}}{{{{\left( {n + 1} \right)}^{a - 1}}\left[ {\left( {na + 2} \right) + ......\left( {na + n} \right)} \right]}} = \frac{1}{{60}}\) for some positive real number \(a\), then \(a\) is equal toJEE Mains 2017 Hard
- Let \(f\) be a real valued continuous function on \([0,1]\) and \(f(x)=x+\int\limits_{0}^{1}(x-t) f(t) d t\). Then which of the following points \(( x , y )\) lies on the curve \(y =f( x )\) ?JEE Mains 2022 Hard
More PYQs from JEE Mains
- If \(A=\left(\begin{array}{cc}\frac{1}{\sqrt{5}} & \frac{2}{\sqrt{5}} \\ \frac{-2}{\sqrt{5}} & \frac{1}{\sqrt{5}}\end{array}\right), B=\left(\begin{array}{ll}1 & 0 \\ i & 1\end{array}\right), i=\sqrt{-1}\), and \(\mathrm{Q}=\mathrm{A}^{\mathrm{T}} \mathrm{BA}\), then the inverse of the matrix \(\mathrm{A} \mathrm{Q}^{2021} \mathrm{~A}^{\mathrm{T}}\) is equal to :JEE Mains 2021 Hard
- If \(\frac{d y}{d x}=\frac{2^{x+y}-2^{x}}{2^{y}}, y(0)=1\), then \(y(1)\) is equal to :JEE Mains 2021 Hard
- Let \(S={\theta \in\left(0, \frac{\pi}{2}\right): \sum_{m=1}^{9}}\) \(\sec \left(\theta+(m-1) \frac{\pi}{6}\right) \sec \left(\theta+\frac{m \pi}{6}\right)=-\frac{8}{\sqrt{3}}\) Then.JEE Mains 2022 Hard
- The number of 6-letter words, with or without meaning, that can be formed using the letters of the word MATHS such that any letter that appears in the word must appear at least twice, is _______.JEE Mains 2025 Medium
- Let the product of the focal distances of the point \(\left(\sqrt{3}, \frac{1}{2}\right)\) on the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,(\mathrm{a}\gt\mathrm{b})\), be \(\frac{7}{4}\). Then the absolute difference of the eccentricities of two such ellipses isJEE Mains 2025 Hard
- If \(\lim _{x \rightarrow \infty}\left(\left(\frac{\mathrm{e}}{1-\mathrm{e}}\right)\left(\frac{1}{\mathrm{e}}-\frac{x}{1+x}\right)\right)^x=\alpha\), then the value of \(\frac{\log _{\mathrm{e}} \alpha}{1+\log _{\mathrm{e}} \alpha}\) equals :JEE Mains 2025 Medium