AP EAMCET · Maths · Three Dimensional Geometry
The direction cosines of the normal drawn to the plane passing through the points \((2,-1,5),(1,-3,4),(5,2,1)\) are
- A \(\frac{11}{\sqrt{179}}, \frac{-7}{\sqrt{179}}, \frac{3}{\sqrt{179}}\)
- B \(\frac{9}{\sqrt{134}}, \frac{-7}{\sqrt{134}}, \frac{2}{\sqrt{134}}\)
- C \(\frac{11}{\sqrt{179}}, \frac{7}{\sqrt{179}}, \frac{-3}{\sqrt{179}}\)
- D \(\frac{9}{\sqrt{134}}, \frac{7}{\sqrt{134}}, \frac{-2}{\sqrt{134}}\)
Answer & Solution
Correct Answer
(A) \(\frac{11}{\sqrt{179}}, \frac{-7}{\sqrt{179}}, \frac{3}{\sqrt{179}}\)
Step-by-step Solution
Detailed explanation
Let \(A=(2,-1,5)\) and \(C=(5,2,1)\) \(\therefore\) Equation of plane passing through \(A, B, C\) is…
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 length of the chord \(2 x+3 y+k=0\) of the circle \(x^2+y^2-6 x-8 y+9=0\) is \(2 \sqrt{3}\), then one of the values of \(\mathrm{k}\) isAP EAMCET 2023 Medium
- \({ }^{34} C_{10}+3 \cdot\left({ }^{34} C_9\right)+3 \cdot\left({ }^{34} C_g\right)+{ }^{34} C_7=\)AP EAMCET 2018 Medium
- \(\int_0^1 x^{5 / 2}(1-x)^{3 / 2} \mathrm{~d} x=\)AP EAMCET 2025 Medium
- \(\int \frac{1+x+\sqrt{x+x^2}}{\sqrt{x}+\sqrt{1+x}} d x\) is equal toAP EAMCET 2003 Medium
- The general solution of the differential equation \(y y^{\prime}=x\left[\frac{y^2}{x^2}+\frac{\phi\left(\frac{y^2}{x^2}\right)}{\phi^{\prime}\left(\frac{y^2}{x^2}\right)}\right]\), where \(\phi\) is an arbitrary function, isAP EAMCET 2019 Easy
- When the coordinate axes are rotated about the origin in the positive direction through an angle \(\frac{\pi}{4}\), if the equation \(25 x^2+9 y^2=225\) is transformed to \(\alpha x^2+\beta x y+\gamma y^2=\delta\), then \((\alpha+\beta+\gamma-\sqrt{\delta})^2=\)AP EAMCET 2019 Hard
More PYQs from AP EAMCET
- At a certain temperature and at infinite dilution, the equivalent conductances of sodium benzoate, hydrochloric acid and sodium chloride are 240, 349 and \(229 \mathrm{ohm}^{-1} \mathrm{~cm}^2\) equiv \(^{-1}\) respectively. The equivalent conductance of benzoic acid in \(\mathrm{ohm}^{-1} \mathrm{~cm}^2\) equiv \(^{-1}\) at the same conditions isAP EAMCET 2010 Easy
- Which of the following practices will not come under green chemistry?
AP EAMCET 2021 Easy - If \(\theta\) is the angle between the curves \(x y=2\) and \(x^2+4 y=0\) and \(x^2+4 y=0\), then \(\tan \theta\) is equal to :AP EAMCET 2006 Medium
- If \(f: R \rightarrow R\) and \(g: R \rightarrow R\) are defined by \(f(x)=|x|\) and \(g(x)=[x-3]\) for \(x \in R\), then \(\left\{g(f(x)):-\frac{8}{5} < x < \frac{8}{5}\right\}\) is equal toAP EAMCET 2008 Medium
- The amplitudes of a damped harmonic oscillator after 2 and 4 seconds are \(A_1\) and \(A_2\) respectively. If the initial amplitude of the oscillator is \(\mathrm{A}_0\), thenAP EAMCET 2023 Hard
- If \(y=(1+x)\left(1+x^2\right)\left(1+x^4\right) \ldots\left(1+x^{2 n}\right)\), then \(\left(\frac{d y}{d x}\right)_{x=0}\) is equal toAP EAMCET 2011 Medium