AP EAMCET · Maths · Three Dimensional Geometry
In \(\triangle A B C\) the mid points of the sides \(A B, B C\) and \(C A\) are respectively \((l, 0,0),(0, m, 0)\) and \((0,0, n)\). Then, \(\frac{A B^2+B C^2+C A^2}{l^2+m^2+n^2}\) is equal to
- A \(2\)
- B \(4\)
- C \(8\)
- D \(16\)
Answer & Solution
Correct Answer
(C) \(8\)
Step-by-step Solution
Detailed explanation
From the figure, \[ \begin{gathered} x_1+x_2=2 l, y_1+y_2=0, z_1+z_2=0, \\ x_2+x_3=0, y_2+y_3=2 m, z_2+z_3=0 \\ \text { and } \quad x_1+x_3=0, y_1+y_3=0, z_1+z_3=2 n \end{gathered} \] On solving, we get…
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 length of the latusrectum of the parabola \(20\left(x^2+y^2-6 x-2 y+10\right)=(4 x-2 y-5)^2\), isAP EAMCET 2019 Easy
- Let \(A, B\) and \(C\) is three points on a circle of radius \(R\), if \(O\) is the centre of the circle and \(\angle A O B=45^{\circ}, \angle B O C=45^{\circ}\), then the resultant of \(\mathbf{O A}, \mathbf{O B}\) and \(\mathbf{O C}\) has magnitudeAP EAMCET 2021 Easy
- The integrating factor of the linear differential equation \(\frac{d y}{d x}=\frac{1}{4 x+3 y}\) isAP EAMCET 2023 Easy
- If \(A\) and \(B\) are two events such that \(P(B) \neq 0\) and \(P(B) \neq 1\), then \(P(\bar{A} \mid \bar{B})\) isAP EAMCET 2022 Easy
- The equation of the ellipse with its focus at \((6,2)\) centre at \((1,2)\) and which passes through the point \((4,6)\) isAP EAMCET 2020 Medium
- The sum of the rational terms in the expansion of \((\sqrt{2}+\sqrt[5]{3})^{10}\) isAP EAMCET 2017 Medium
More PYQs from AP EAMCET
- In hydrogen atom, if an electron in the orbit with principal quantum number ' \(n\) ' jumps to the first excited state, the wavelength of the emitted photon is ' \(\lambda\) '. Then the value of \(\mathrm{n}\) is
(R-Rydberg constant)AP EAMCET 2023 Medium - In a nuclear reactor, the fuel is consumed at the rate of \(1 \times 10^{-3} \mathrm{gs}^{-1}\). The power generated in kW isAP EAMCET 2024 Medium
- Two charges each of charge \(+10 \mu C\) are kept on \(Y\)-axis at \(y=-a\) and \(y=+a\), respectively. Another point charge \(-20 \mu C\) is placed at the origin and given a small displacement \(x(x< < a)\) along \(X\)-axis. The force acting on the point charge is
\(\left(x \text { and } a \text { are in metres, } \frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{~N}-\mathrm{m}^2 \mathrm{C}^{-2}\right)\)AP EAMCET 2016 Easy - Let \(z_1, z_2\) be two complex numbers such that \(\bar{z}_1-i \bar{z}_2=0\) and \(\arg \left(z_1 z_2\right)=\frac{3 \pi}{4}\), then \(\arg \left(z_1\right)=\)AP EAMCET 2020 Easy
- The function \(f: C \rightarrow C\) defined by \(f(x)=\frac{a x+d}{c x+d}\) for \(x \in C\) where \(b d \neq 0\) reduces to a constant function, ifAP EAMCET 2005 Easy
- If the lines, joining the origin to the points of intersection of the curve and the line , are at right angles, then equalsAP EAMCET 2021 Hard