JEE Mains · Maths · STD 12 - 11. three dimension geometry
The distance of the point \((1, -2, 4)\) from the plane passing through the point \((1, 2, 2 )\) and perpendicular to the planes \(x - y + 2 z = 3\) and \(2x - 2y+ z+ 12=0,\) is
- A \(2\)
- B \(\sqrt 2\)
- C \(2\sqrt 2\)
- D \(\frac {1}{\sqrt 2}\)
Answer & Solution
Correct Answer
(C) \(2\sqrt 2\)
Step-by-step Solution
Detailed explanation
Let equation of plane be \(a(x-1)+b(y-2)+c(z-2)=0\) .....\((1)\) \((1)\) is perpendicular to given planes then \(a-b+2 c=0\) \(2 a-2 b+c=0\) Solving above equation \(c=0\) and \(a=b\) equation of plane \(( 1)\) can be \(x+y-3=0\) distance from \((1,-2,4)\) will be…
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
- For a statistical data \(\mathrm{x}_1, \mathrm{x}_2, \ldots, \mathrm{x}_{10}\) of 10 values, a student obtained the mean as 5.5 and \(\sum_{i=1}^{10} x_i^2=371\). He later found that he had noted two values in the data incorrectly as 4 and 5 , instead of the correct values 6 and 8 , respectively. The variance of the corrected data isJEE Mains 2025 Medium
- If \((2,3,9),(5,2,1),(1, \lambda, 8)\) and \((\lambda, 2,3)\) are coplanar, then the product of all possible values of \(\lambda\) is.JEE Mains 2022 Hard
- Let \( S = \{t \in R : f(x)= |x-\pi|.(e^{|x|}-1)sin|x|\) is not differentiable at \(t\,\,\}\). Then the set \(S\) is equal to :JEE Mains 2018 Hard
- Let a triangle \(A B C\) be inscribed in the circle \(x ^{2}-\) \(\sqrt{2}(x+y)+y^{2}=0\) such that \(\angle B A C=\frac{\pi}{2}\). If the length of side \(A B\) is \(\sqrt{2}\), then the area of the \(\triangle ABC\) is equal toJEE Mains 2022 Medium
- Let \(A=\left[\begin{array}{cc}1 & \frac{1}{51} \\ 0 & 1\end{array}\right]\). If \(B=\left[\begin{array}{cc}1 & 2 \\ -1 & -1\end{array}\right] A \left[\begin{array}{cc}-1 & -2 \\ 1 & 1\end{array}\right]\) then the sum of all the elements of the matrix \(\sum \limits_{n=1}^{50} B^n\) is equal toJEE Mains 2023 Hard
- If \((\sqrt{3}+\mathrm{i})^{100}=2^{99}(\mathrm{p}+\mathrm{i} \mathrm{q})\), then \(\mathrm{p}\) and \(\mathrm{q}\) are roots of the equation :JEE Mains 2021 Hard
More PYQs from JEE Mains
- Consider the matrices \(A = \begin{bmatrix} 2 & -2 \\ 4 & -2 \end{bmatrix}\) and \(B = \begin{bmatrix} 3 & 9 \\ 1 & 3 \end{bmatrix}\). If matrices P and Q are such that \(PA = B\) and \(AQ = B\), then the absolute value of the sum of the diagonal elements of \(2(P + Q)\) is _______.JEE Mains 2026 Hard
- The area (in sq. units) in the first quadrant bounded by the parabola, \(y = x^2 +1\), the tangent to it at the point \((2, 5)\) and the coordinate axes isJEE Mains 2019 Hard
- Let \(p , q \in R\) and \((1-\sqrt{3} i )^{200}=2^{199}( p + iq )\), \(i =\sqrt{-1}\) Then \(p + q + q ^2\) and \(p - q + q ^2\) are roots of the equation.JEE Mains 2023 Hard
- Let \(A =\{1,2,3, \ldots, 10\}\) and \(f: A \rightarrow A\) be defined as \(f( k )=\left\{\begin{array}{cl} k +1 & \text { if } k \text { is odd } \\ k & \text { if } k \text { is even }\end{array}\right.\) Then the number of possible functions \(g : A \rightarrow A\) such that \(gof=f\) is ...... .JEE Mains 2021 Medium
- If the maximum distance of normal to the ellipse \(\frac{x^2}{4}+\frac{y^2}{b^2}=1, b < 2\), from the origin is \(1\) , then the eccentricity of the ellipse is:JEE Mains 2023 Hard
- Let \(A B C D\) be a trapezium whose vertices lie on the parabola \(y^2=4 x\). Let the sides \(A D\) and \(B C\) of the trapezium be parallel to y -axis. If the diagonal AC is of length \(\frac{25}{4}\) and it passes through the point \((1,0)\), then the area of \(A B C D\) isJEE Mains 2025 Medium