JEE Mains · Maths · STD 12 - 11. three dimension geometry
If the mirror image of the point \((1,3,5)\) with respect to the plane \(4 x -5 y +2 z =8\) is \((\alpha, \beta, \gamma)\) then \(5(\alpha+\beta+\gamma)\) equals ...... ..
- A \(47\)
- B \(43\)
- C \(39\)
- D \(41\)
Answer & Solution
Correct Answer
(A) \(47\)
Step-by-step Solution
Detailed explanation
Point \(Q\) is image of point \(P\) w.r.to plane, \(M\) is mid point of \(P\) and \(Q\), lies in plane \(M \left(\frac{1+\alpha}{2}, \frac{3+\beta}{2}, \frac{5+\gamma}{2}\right)\) \(4 x-5 y+2 z=8\)…
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
- If the number of five digit numbers with distinct digits and \(2\) at the \(10^{\text {th }}\) place is \(336 \mathrm{k}\), then \(\mathrm{k}\) is equal toJEE Mains 2020 Hard
- \(\lim \limits_{x \rightarrow 0}\left(\tan \left(\frac{\pi}{4}+x\right)\right)^{\frac{1}{x}}\) is equal toJEE Mains 2020 Medium
- The sum of all real values of \(x\) for which \(\frac{3 x^{2}-9 x+17}{x^{2}+3 x+10}=\frac{5 x^{2}-7 x+19}{3 x^{2}+5 x+12}\) is equal to.JEE Mains 2022 Hard
- Let \(I(x)=\int \frac{6}{\sin ^2 x(1-\cot x)^2} d x\). If \(I(0)=3\), then \(\mathrm{I}\left(\frac{\pi}{12}\right)\) is equal to :JEE Mains 2024 Hard
- The value of \(\frac{8}{\pi} \int \limits_0^{\frac{\pi}{2}} \frac{(\cos x)^{2023}}{(\sin x)^{2023}+(\cos x)^{2023}} d x\) is \(.............\).JEE Mains 2023 Easy
- Let \(\mathrm{a}, \mathrm{b}, \mathrm{c} \in \mathrm{N}\) and \(\mathrm{a}<\mathrm{b}<\mathrm{c}\). Let the mean, the mean deviation about the mean and the variance of the \(5\) observations \(9\),\(25\), \(a\), \(b\), \(c\) be \(18\),\(4\) and \(\frac{136}{5}\), respectively. Then \(2 \mathrm{a}+\mathrm{b}-\mathrm{c}\) is equal to ..............JEE Mains 2024 Hard
More PYQs from JEE Mains
- \(\mathop {\lim }\limits_{y \to 0} \frac{{\sqrt {1 + \sqrt {1 + {y^4}} } - \sqrt 2 }}{{{y^4}}} = \)JEE Mains 2019 Hard
- Let \(P\) and \(Q\) be the points on the line \(\frac{x+3}{8}=\frac{y-4}{2}=\frac{z+1}{2}\) which are at a distance of \(6\) units from the point \(R(1,2,3)\). If the centroid of the triangle \(PQR\) is \((\alpha, \beta, \gamma)\), then \(\alpha^2+\beta^2+\gamma^2\) is :JEE Mains 2024 Hard
- An ordered pair \((\alpha , \beta )\) for which the system of linear equations \(\left( {1 + \alpha } \right)x + \beta y + z = 2\) ; \(\alpha x + \left( {1 + \beta } \right)y + z = 3\) ; \(\alpha x + \beta y + 2z = 2\) has a unique solution, isJEE Mains 2019 Hard
- Let \(A=\left[\begin{array}{ccc}\cos \theta & 0 & -\sin \theta \\ 0 & 1 & 0 \\ \sin \theta & 0 & \cos \theta\end{array}\right]\). If for some \(\theta \in(0, \pi)\), \(A^2=A^T\), then the sum of the diagonal elements of the matrix \((\mathrm{A}+\mathrm{I})^3+(\mathrm{A}-\mathrm{I})^3-6 \mathrm{~A}\) is equal to _____ .JEE Mains 2025 Easy
- Let \(\alpha\) and \(\beta\) be the roots of the equation \(x^{2}+(2 i -\) \(1)=0\). Then, the value of \(\left|\alpha^{8}+\beta^{8}\right|\) is equal toJEE Mains 2022 Medium
- If the system of linear equations \(x_1 + 2x_2 + 3x_3 = 6\) ; \(x_1 + 3x_2 + 5x_3 = 9\) ; \(2x_1 + 5x_2 + ax_3 = b\) is consistent and has infinite number of solutions, thenJEE Mains 2013 Hard