TS EAMCET · Maths · Three Dimensional Geometry
If the points \(A(-1,0,7), B(3,2, t), C(5, k,-2)\) are collinear, then the ratio in which the point \(P(t, k-2 t, t+k)\) divides the line segment \(B C\) is
- A \(-2: 3\)
- B \(-1: 2\)
- C \(4: 3\)
- D \(1: 1\)
Answer & Solution
Correct Answer
(B) \(-1: 2\)
Step-by-step Solution
Detailed explanation
We have, \(A(-1,0,7), B(3,2, t)\) and \(C(5, k,-2)\) are collinear. \(\therefore \quad \frac{3+1}{5-3}=\frac{2-0}{k-2}=\frac{t-7}{-2-t}\)…
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 circle \(x^2+y^2+2 x+3 y+1=0\) cuts another circle \(x^2+y^2+4 x+3 y+2=0\) in \(A\) and \(B\), then the equation of the circle with \(A B\) as a diameter isTS EAMCET 2010 Hard
- If \(f: \mathbb{R} \rightarrow \mathbb{R}\) is defined by \(f(\mathrm{x})=2 \mathrm{x}+\sin \mathrm{x}, \mathrm{x} \in \mathrm{R}\), then \(f\) isTS EAMCET 2023 Medium
- A man has 7 relatives, 4 of them are ladies and 3 gents; his wife has 7 other relatives, 3 of them are ladies and 4 gents. The number of ways they can invite them to a party of 3 ladies and 3 gents so that there are 3 of man's relatives and 3 of wife's relatives, isTS EAMCET 2024 Medium
- If \(b+c=3 a\), then \(\cot \frac{B}{2} \cot \frac{C}{2}\) is equal to :TS EAMCET 2006 Hard
- If \(\tan (\pi \cos \theta)=\cot (\pi \sin \theta)\), then a value of \(\cos \left(\theta-\frac{\pi}{4}\right)\) among the following isTS EAMCET 2013 Medium
- The equation of the circle of radius 3 that lies in the fourth quadrant and touching the lines \(x=0\) and \(y=0\) isTS EAMCET 2007 Medium
More PYQs from TS EAMCET
- The point \((3,2)\) undergoes the following three transformations in the order given (i) Reflection about the line \(y=x\). (ii) Translation by the distance 1 unit in the positive direction of \(x\)-axis. (iii) Rotation by an angle \(\frac{\pi}{4}\) about the origin in the anti-clockwise direction. Then, the final position of the point isTS EAMCET 2012 Medium
- If the pair of straight lines \(x y-x-y+1=0\) and the line \(a x+2 y-3 a=0\) are concurrent, then \(a\) is equal toTS EAMCET 2002 Medium
- Which purification method is generally used for a high boiling organic liquid compound, which decompose below its boiling point?TS EAMCET 2025 Medium
- If the function \(\mathrm{f}(\mathrm{x})=\mathrm{xe}^{-\mathrm{x}}, \mathrm{x} \in \mathbb{R}\) attains its maximum value \(\beta\) at \(x=\alpha\) then \((\alpha, \beta)=\)TS EAMCET 2023 Easy
- The correct order of rates of \(\mathrm{C}-\mathrm{Br}\) bond ionisation of the following bromides is:
TS EAMCET 2019 Medium - A plane \(x\) passes through the point \((1,1,1)\). If \(b, c, a\) are the direction ratios of a normal to the plane, where \(a, b, c(a < b < c)\) are the factors of 2001 , then the equation of the plane isTS EAMCET 2002 Medium