MHT CET · Maths · Straight Lines
If \(G(\bar{g}), H(\bar{h})\) and \(P(\bar{p})\) are respectively centroid, orthocenter and circumcentre of a triangle and \(x \bar{p}+y \bar{h}+z \bar{g}=\overline{0}\), then \(x, y, z\) are respectively.
- A \(1,1,-2\)
- B \(1,3,-4\)
- C \(2,1,-3\)
- D \(2,3,-5\)
Answer & Solution
Correct Answer
(C) \(2,1,-3\)
Step-by-step Solution
Detailed explanation
We know that centroid divides a line joining orthocenter to circumcentre in the ratio \(2: 1\).
\(\therefore \overline{\mathrm{g}}=\frac{\overline{\mathrm{h}}+2 \overline{\mathrm{p}}}{1+2} \Rightarrow 2 \overline{\mathrm{p}}+\overline{\mathrm{h}}=-3 \overline{\mathrm{g}}\)
\(\therefore \mathrm{x}=2, \mathrm{y}=1, \mathrm{z}=-3 \text { as per data given.}\)
\(\therefore \overline{\mathrm{g}}=\frac{\overline{\mathrm{h}}+2 \overline{\mathrm{p}}}{1+2} \Rightarrow 2 \overline{\mathrm{p}}+\overline{\mathrm{h}}=-3 \overline{\mathrm{g}}\)
\(\therefore \mathrm{x}=2, \mathrm{y}=1, \mathrm{z}=-3 \text { as per data given.}\)
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
- For statement; If a quadrilateral \(A B C D\) is a rhombus then its opposite sides are parallel", its contrapositive and converse are respectively given byMHT CET 2022 Easy
- A family with three children is chose at random. The probability that the oldest and youngest children are of the same gender isMHT CET 2022 Easy
- A man is know to speak truth 3 out of 4 times. He throws a die and reports that it is 6 . Then the probability that it is actually 6 isMHT CET 2021 Medium
- If the line \(x-2 y=\mathrm{m}(\mathrm{m} \in \mathrm{Z})\) intersects the circle \(x^2+y^2=2 x+4 y\) at two distinct points, then the number of possible values of \(\mathrm{m}\) areMHT CET 2023 Medium
- If \(A=\left[\begin{array}{ccc}0 & 1+2 i & i-2 \\ -1-2 i & 0 & K \\ 2-1 & 7 & 0\end{array}\right]\) and \(A^{-1}\) does not exists, then \(K=\) (where \(\mathrm{i}=\sqrt{-1}\) )MHT CET 2022 Easy
- If \(P=\left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right]\) is the adjoint of a \(3 \times 3\) matrix A and \(|A|=4\), then value of \(\alpha\) isMHT CET 2023 Easy
More PYQs from MHT CET
- The weight of a man in a lift moving upwards with an acceleration ' \(a\) ' is \(620 \mathrm{~N}\). When the lift moves downwards with the same acceleration, his weight is found to be \(340 \mathrm{~N}\). The real weight of the man isMHT CET 2021 Medium
- A molecule of water on the surfaceMHT CET 2019 Medium
- Which of the following can absorb over \(90 \%\) of its own mass of water and also does not stick to wounds?MHT CET 2011 Medium
- Which among the following is a linear polymer?MHT CET 2020 Easy
- A standing wave having 3 nodes and 2 antinodes is formed between two atoms having a distance \(1.21 Å\) Å between them. The wavelength of the standing wave isMHT CET 2007 Medium
- The conversion of 2- methylpropan – 1 – ol to 2- methylpropan -2- ol isMHT CET 2019 Easy