AP EAMCET · Maths · Three Dimensional Geometry
Let \(P\left(x_1, y_1, z_1\right)\) be the foot of perpendicular drawn from the point \(Q(2,-2,1)\) to the plane \(x-2 y+z=1\). If \(d\) is the perpendicular from the point \(Q\) to the plane and \(l=x_1+y_1+z_1\), then \(l+3 d^2\) is
- A 5
- B 7
- C 19
- D 26
Answer & Solution
Correct Answer
(C) 19
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { } \frac{x_1-2}{1}=\frac{y_1+2}{-2}=\frac{z_1-1}{1}=\frac{-(2+4+1-1)}{6} \\ & x_1=1, y_1=0, z_1=0 \Rightarrow l=1+0+0=1 \\ & d=\left|\frac{2+4+1-1}{\sqrt{6}}\right|=\sqrt{6} \\ & \Rightarrow l+3 d^2=19\end{aligned}\)
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
- \(\operatorname{In} \frac{x^4-6 x^3+9 x^2+5 x-20}{x^2-x-2}=f(x)+\frac{a}{x+p}+\frac{b}{x+q}\) then \(2(a+b)=\)AP EAMCET 2023 Medium
- If a directrix of a hyperbola centred at the origin and passing through the point \((4,-2 \sqrt{3})\) is \(\sqrt{5} x=4\) and \(e\) is its eccentricity, then \(e^2=\)AP EAMCET 2024 Easy
- The number of integer solutions of the equation isAP EAMCET 2022 Hard
- If \(\quad u=\log \left(x^3+y^3+z^3-3 x y z\right), \quad\) then \((x+y+z)\left(u_x+u_y+u_z\right)\) is equal toAP EAMCET 2013 Hard
- If all chords of the curve \(2 x^2-y^2+3 x+2 y=0\), which subtend a right angle at the origin always passing through the point \((\alpha, \beta)\), then \((\alpha, \beta)=\)AP EAMCET 2024 Easy
- If the function \(f(x)=a x^3+b x^2+11 x-6\) satisfies the conditions of Rolle's theorem in \([1,3]\) and \(f^{\prime}\left(2+\frac{1}{\sqrt{3}}\right)=0\), then \(a+b=\)AP EAMCET 2019 Easy
More PYQs from AP EAMCET
- If \(\int\left(\frac{4 e^x+6 e^{-x}}{9 e^x-4 e^{-x}}\right) d x=A x+B \log \left|\left(9 e^{2 x}-4\right)\right|+C\), then \((\mathrm{A}, \mathrm{B})=\)AP EAMCET 2023 Medium
- In an adsorption experiment, a graph between versus was found to be linear with a slope of . The intercept on axis was found to be . The amount of gas adsorbed per gram of charcoal under a pressure of isAP EAMCET 2021 Easy
- The IUPAC name of the compound \(\left(\mathrm{CH}_3\right)_2 \mathrm{CH}-\mathrm{CH}=\mathrm{CH}-\mathrm{CHOH}-\mathrm{CH}_3\) isAP EAMCET 2007 Easy
- If the angle \(2 \theta\) is acute, then the acute angle between the pair of straight lines
\[
\begin{aligned}
& x^2(\cos \theta-\sin \theta)+2 x y \cos \theta \\
& \quad+y^2(\cos \theta+\sin \theta)=0, \text { is }
\end{aligned}
\]AP EAMCET 2002 Hard - Two particles of masses \(m\) and \(2 m\) have equal kinetic energies. The de-Broglie wavelengths are in the ratio ofAP EAMCET 2021 Easy
- A straight line which makes equal intercepts on positive \(X\) and \(Y\) axes and which is at a distance 1 unit from the origin intersects the straight line \(y=2 x+3+\sqrt{2}\) at \(\left(x_0, y_0\right)\). Then \(2 x_0+y_0\) is equal toAP EAMCET 2010 Hard