AP EAMCET · Maths · Three Dimensional Geometry
The equation of the plane bisecting the line segment joining the points \((2,0,6)\) and \((-6,2,4)\) and perpendicular to it, is
- A \(2 x-y+4 z-15=0\)
- B \(4 x-y+3 z-6=0\)
- C \(4 x-y+z+4=0\)
- D \(x-2 y+3 z-11=0\)
Answer & Solution
Correct Answer
(C) \(4 x-y+z+4=0\)
Step-by-step Solution
Detailed explanation
Let variable point on the plane is \((x, y, z)\). Mid-point of the line segment joining the points \((2,0,6)\) and \((-6,2,4)=(-2,1,5)\) Direction ratio of the line segment joining the points \((2,0,6)\) and \((-6,2,4)\) \[ \Rightarrow(-6-2),(2-0),(4-6)-8,2,-2=a_1, b_1, c_1 \]…
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 \(x\) is positive real number and the first negative term in the expansion of \((1+\mathrm{x})^{27 / 5}\) is \(\mathrm{t}_{\mathrm{k}}\) then \(\mathrm{k}=\)AP EAMCET 2025 Medium
- A plane is making intercepts \(2,3,4\) on \(X, Y\) and \(Z\)-axes respectively. Another plane is passing through the point \((-1,6,2)\) and is perpendicular to the line joining the points \((1,2,3)\) and \((-2,3,4)\). Then angle between the two planes isAP EAMCET 2019 Hard
- The normal drawn at a point \((2,-4)\) on the parabola \(y^2=8 x\) cuts again the same parabola at \((\alpha, \beta)\) then \(\alpha+\beta=\)AP EAMCET 2024 Medium
- The derivative of \(\operatorname{Sec}^{-1}\left(\frac{1}{2 x^2-1}\right)\) with respect to \(\sqrt{1-x^2}\) at \(x=\frac{1}{2}\) isAP EAMCET 2025 Medium
- A point \(C\) with position vector \(\frac{3 \bar{a}+4 \bar{b}-5 \bar{c}}{3}\) (where \(\bar{a}, \bar{b}\) and \(\bar{c}\) are non coplanar vectors) divides the line joining \(A\) and \(B\) in the ratio \(2: 1\). If the position vector of \(A\) is \(\bar{a}-2 \bar{b}+3 \bar{c}\), then the position vector of \(B\) isAP EAMCET 2017 Easy
- If 5 letters are to be placed in 5 -addressed envelopes, then the probability that at least one letter is placed in the wrongly addressed envelope isAP EAMCET 2024 Easy
More PYQs from AP EAMCET
- What is the value ofAP EAMCET 2021 Medium
- The solubility products of three sparingly soluble salts \(A B, A_2 B\) and \(A B_3\) are respectively \(4.0 \times 10^{-20}, 3.2 \times 10^{-11}\) and \(2.7 \times 10^{-31}\).
The increasing order of their solubility isAP EAMCET 2018 Easy - A body is moving along a straight line under the influence of a constant power source. If the relation between the displacement \((\mathrm{s})\) of the body and time \((\mathrm{t})\) is \(s \propto t^x\), then \(x=\)AP EAMCET 2025 Medium
- The incenter of the triangle formed by the points \((0,0,0),(3,0,0)\) and \((0,4,0)\) isAP EAMCET 2021 Easy
- Observe the following statements
i. The dipole moment of \(\mathrm{NH}_3\) is higher than the dipole moment of \(\mathrm{NF}_3\).
ii. The dipole moment of chloroform is zero.
iii. Covalent bond character in \(\mathrm{NaCl}\) is more compared to \(\mathrm{CuCl}\).AP EAMCET 2018 Easy - If \(\cos A+\cos (A+B)+\cos (A+2 B)+\ldots\) upto \(n\) terms \(=\) \(\cos \left(\frac{2 \mathrm{~A}+(\mathrm{n}-1) \mathrm{B}}{2}\right) \sin \frac{\mathrm{nB}}{2} \operatorname{cosec} \frac{\mathrm{B}}{2}\),
then \(\cos \frac{\pi}{19}+\cos \frac{3 \pi}{19}+\cos \frac{5 \pi}{19}+\ldots+\cos \frac{17 \pi}{19}=\)AP EAMCET 2023 Medium