AP EAMCET · Maths · Vector Algebra
Consider the tetrahedron with the vertices \(\mathrm{A}(3,2,4)\), \(\mathrm{B}\left(x_1, y_1, 0\right), \mathrm{C}\left(x_2, y_2, 0\right), \mathrm{D}\left(x_3, y_3, 0\right)\). If the triangle BCD is formed by the lines \(y=x, x+y=6\) and \(\mathrm{y}=1\), then the centroid of the tetrahedron is
- A \(\left(\frac{9}{4}, \frac{7}{4}, 1\right)\)
- B \(\left(\frac{11}{4}, \frac{5}{4}, 1\right)\)
- C \(\left(3, \frac{7}{4}, 1\right)\)
- D \((3,2,1)\)
Answer & Solution
Correct Answer
(C) \(\left(3, \frac{7}{4}, 1\right)\)
Step-by-step Solution
Detailed explanation
\(\mathrm{A}(3,2,4), \mathrm{B}\left(x_1, y_1, 0\right), \mathrm{C}\left(x_2, y_2, 0\right), \mathrm{D}\left(x_3, y_3, 0\right)\) \(\triangle \mathrm{BCD}\) is formed by lines \(y=x, x+y=6, y=1\) \(\therefore\) Vertices of BCD are D \((1,1), \mathrm{C}(3,3), \mathrm{D}(5,1)\)…
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 \(X=x+h, Y=y+k\) transforms \(\frac{d y}{d x}=\frac{2 x+3 y-7}{3 x+2 y-8}\) to a homogeneous differential equation, then \((\mathrm{h}, \mathrm{k})=\)AP EAMCET 2023 Medium
- \(\text { If } \tan ^{-1} x+\tan ^{-1} y+\tan ^{-1} z=\frac{\pi}{2}\)
then \(1-x y-y z-z x\) is equal toAP EAMCET 2010 Medium - If \(I_n=\int(\log x)^n d x\), then \(I_n+n I_{n-1}=\)AP EAMCET 2020 Medium
- For and . If and thenAP EAMCET 2022 Hard
- If \(\lim _{x \rightarrow 0} \frac{e^x-a-\log (1+x)}{\sin x}=0\) then \(a=\)AP EAMCET 2024 Easy
- A circle \(S \equiv x^2+y^2-16=0\) intersects another circle \(S^{\prime}=0\) of radius 5 units such that their common chord is of maximum length. If the slope of that chord is \(\frac{3}{4}\), then the centre of such a circle \(S^{\prime}=0\) isAP EAMCET 2025 Medium
More PYQs from AP EAMCET
- are roots of the cubic equation given byAP EAMCET 2021 Medium
- The frequency of ac at which \(16 \mu \mathrm{F}\) capacitor and \(\frac{10}{\pi^2}\) \(\mathrm{mH}\) inductor will have same reactance isAP EAMCET 2023 Easy
- Which of the following occurs with \(\mathrm{KMnO}_4\) in neutral medium?AP EAMCET 2024 Medium
- The linear shape of \(\mathrm{CO}_2\) is due toAP EAMCET 2020 Easy
- In \(\triangle \mathrm{ABC}\) the coordinates of the vertex \(\mathrm{A}\) are \((-3,1)\). If the equation of the median through \(B\) is \(2 x+y-3=0\) and the equation of the bisector of angle \(\mathrm{C}\) is \(7 \mathrm{x}-4 \mathrm{y}-1=0\), then the equation of the side \(\mathrm{BC}\) isAP EAMCET 2023 Easy
- In the circuit shown in the figure, the current ' \(T\) ' is
AP EAMCET 2013 Easy