AP EAMCET · Maths · Straight Lines
The points and are
- A collinear
- B vertices of a right-angled triangle
- C vertices of an equilateral triangle
- D vertices of an isosceles triangle
Answer & Solution
Correct Answer
(A) collinear
Step-by-step Solution
Detailed explanation
Let a lineAC divides at B in ratio m:n A(2,3,4),B-1,-2,1 & C5,8,7 So (-1,2,1)=mx2+nx1m+n,my2+ny1m+n,mz2+nz1m+n ⇒-1,2,1=5m+2nm+n,8m+nm+n,7m+4nm+n ⇒-1=5m+2nm+n,-2=8m+nm+n,1=7m+4nm+n ⇒mn=-12,mn=-12,mn=-12 Ratio are same. It means points are collinear.
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 \(\mathrm{O}(0,0,0), \mathrm{A}(3,0,0), \mathrm{B}(0,4,0)\) form a triangle then the incentre of triangle OAB isAP EAMCET 2024 Medium
- If the angle between the straight lines joining the foci and the ends of the minor axis of the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) is \(90^{\circ}\), then it eccentricity isAP EAMCET 2022 Medium
- The mean deviation from the mean of the data given below is
\(\begin{array}{|l|l|l|l|l|l|}
\hline \text { Marks: } & 10 & 15 & 20 & 25 & 30 \\
\hline \text { Number of students: } & 2 & 4 & 6 & 8 & 5 \\
\hline
\end{array}\)AP EAMCET 2017 Medium - If \(A\) is in the third quadrant and \(\tan A=\frac{\sqrt{7}}{3}\), then \(18-16 \sin ^2 \frac{A}{2}-32 \sin \frac{A}{2} \sin \frac{5 A}{2}=\)AP EAMCET 2018 Medium
- The set of all values of \(k\) for which the inequality \(x^2-(3 \mathrm{k}+1)\) \(x+4 \mathrm{k}^2+3 \mathrm{k}-3\gt0\) is true for all real values of \(x\) isAP EAMCET 2024 Medium
- A student writes an examination which contains eight true or false questions. If he answers six or more questions correctly, he passes the examination. If the student answers all the questions, then the probability that he fails in the examination isAP EAMCET 2024 Easy
More PYQs from AP EAMCET
- A tank of oil has height of \(4 \mathrm{~m}\) and density of \(850 \mathrm{~kg} \mathrm{~m}^{-3}\). The gauge pressure at the bottom of the tank is (1 atm \(=10^5 \mathrm{~Pa}\), Acceleration due to gravity \(=10 \mathrm{~ms}^{-2}\) )AP EAMCET 2023 Easy
- Identify the correct statement from the following with respect to high density polytheneAP EAMCET 2023 Easy
- If \(\mathrm{t}_{\mathrm{n}}=\frac{1}{4}(\mathrm{n}+2)(\mathrm{n}+3), \mathrm{n} \in \mathrm{N}\), then which one of the following is true?
Assertion (A) : \(\frac{1}{t_1}+\frac{1}{t_2}+\ldots+\frac{1}{t_{2003}}=\frac{2003}{3009}\)
Reason (R) : \(\frac{1}{\mathrm{t}_1}+\frac{1}{\mathrm{t}_2}+\ldots+\frac{1}{\mathrm{t}_{\mathrm{n}}}=\frac{4 \mathrm{n}}{(2 \mathrm{n}+3)}\)AP EAMCET 2025 Medium - The area (in square units) enclosed between the curves \(y=\sin x\) and \(y=\cos x\) for \(\frac{\pi}{4} \leq x \leq \frac{5 \pi}{4}\) isAP EAMCET 2017 Medium
- Calculate \(\Delta H^{\circ}\) for the reaction, \(\mathrm{Na}_2 \mathrm{O}(\mathrm{s})+\mathrm{SO}_3(\mathrm{~g}) \longrightarrow \mathrm{Na}_2 \mathrm{SO}_4(\mathrm{~g})\) given the following :
AP EAMCET 2009 Easy - If \(x\) is so small, that \(x^5\) and higher power of \(x\) may be neglected, then the coefficient of \(x^4\) in the expansion of \(\sqrt{x^2+4}-\sqrt{x^2+9}\), isAP EAMCET 2019 Medium