AP EAMCET · Maths · Three Dimensional Geometry
If \(-2, \frac{4}{3}, \frac{-4}{5}\) are the intercepts made by a plane on \(\mathrm{X}, \mathrm{Y}, \mathrm{Z}\)-axes respectively then the direction cosines of a normal to this plane are
- A \(\left(\frac{-1}{3}, \frac{2}{3}, \frac{-2}{3}\right)\)
- B \(\left(\frac{2}{3 \sqrt{5}}, \frac{-4}{3 \sqrt{5}}, \frac{5}{3 \sqrt{5}}\right)\)
- C \(\left(\frac{-4}{\sqrt{57}}, \frac{4}{\sqrt{57}}, \frac{-5}{\sqrt{57}}\right)\)
- D \(\left(\frac{2}{\sqrt{38}}, \frac{-3}{\sqrt{38}}, \frac{5}{\sqrt{38}}\right)\)
Answer & Solution
Correct Answer
(D) \(\left(\frac{2}{\sqrt{38}}, \frac{-3}{\sqrt{38}}, \frac{5}{\sqrt{38}}\right)\)
Step-by-step Solution
Detailed explanation
If plane makes intercepts \(a, b, c\) then equation of plane is \(\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1\) for \(-2,4 / 3,-4 / 5\), equation of plane 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 line passing through the points \((5,1, a)\) and \((3, b, 1)\) crosses the YZ plane at the point \(\left(0, \frac{17}{2}, \frac{-18}{2}\right)\), then \(a+b=\)AP EAMCET 2023 Medium
- \(\int_{-\pi / 4}^{\pi / 3}\left|\tan \left(x-\frac{\pi}{6}\right)\right| d x=\)AP EAMCET 2025 Medium
- When success is not an impossible event, then the mean of Binomial distribution isAP EAMCET 2022 Easy
- Solve \(\tan (x)+\sec (x)=\sqrt{3}, x \in[0,2 \pi]\)AP EAMCET 2020 Medium
- The domain of the real valued function \(f(x)=\frac{3}{4-x^2}+\log _{10}\left(x^3-x\right)\) isAP EAMCET 2025 Medium
- The distance between the parallel lines \(9 x^2-6 x y+y^2+18 x-6 y+8=0\) isAP EAMCET 2020 Medium
More PYQs from AP EAMCET
- If \(\alpha\) and \(\beta\) are non-real roots of \(x^3-x^2-x-2=0\), then \(\alpha^{2020}+\beta^{2020}+\alpha^{2020} \cdot \beta^{2020}=\)AP EAMCET 2020 Medium
- The mean deviation from the mean for the data \(6,7,10\), \(12,13,4,12,16\) isAP EAMCET 2023 Easy
- Calculate the number of protons, neutrons and electrons in \({ }_{16}^{32} \mathrm{~S}^{2-}\).AP EAMCET 2020 Easy
- Which of the following statement(s) is/are correct?
(i) \(\mathrm{Li} \mathrm{NO} \mathrm{NO}_3, \mathrm{Ba}\left(\mathrm{NO}_3\right)_2\) both will give \(\mathrm{NO}_2\) on heatiing
(ii) \(\mathrm{BaSO}_4\) is less soluble in water than \(\mathrm{CaSO}_4\)
(iii) Alkaline earth metals do not dissolve in liquid ammoniaAP EAMCET 2023 Easy - The magnitude of the axial field due to a short bar magnet at a distance of \(50 \mathrm{~cm}\) from its mid-point is (The magnetic moment of the bar magnet is \(0.4 \mathrm{Am}^2\) )AP EAMCET 2023 Easy
- \(\lim _{n \rightarrow \infty}\left[\frac{n+1}{n^2+1^2}+\frac{n+2}{n^2+2^2}+\frac{n+3}{n^2+3^2}+\ldots+\frac{n+2 n}{n^2+4 n^2}\right]=\)AP EAMCET 2025 Medium