TS EAMCET · Maths · Three Dimensional Geometry
A plane meets the coordinate axes at \(A, B, C\) respectively such that the centroid of the \(\triangle A B C\) is \((2,3,5)\). Then, the equation of that plane is
- A \(3 x+3 y+3 z=10\)
- B \(6 x+9 y+15 z=1\)
- C \(2 x+3 y+5 z=1\)
- D \(15 x+10 y+6 z=90\)
Answer & Solution
Correct Answer
(D) \(15 x+10 y+6 z=90\)
Step-by-step Solution
Detailed explanation
Let the equation of plane is, \(\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1\) where \(a, b, c\) are \(x, y\) and \(z\) intercepts \(\therefore\) Centroid of \(\triangle A B C\) is \(\left(\frac{a}{3}, \frac{b}{3}, \frac{c}{3}\right)\).…
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 circles \(x^2+y^2+2 k x-4 y+1=0\) and \(x^2+y^2-8 x-12 y+43=0\) touch each other then \(k=\)TS EAMCET 2018 Medium
- If the maximum value of \(2 x-7-a x^2\) cannot exceed 20 , then the minimum value of \(a\) isTS EAMCET 2019 Easy
- Consider the following statements Assertion (A) If \(P_1, P_2, P_3\) are probability of happening of three independent events, then probability of happening of atleast one of them is \(1-\left[\left(1-P_1\right)\left(1-P_2\right)\left(1-P_3\right)\right]\) Reason (R) For any three independent events \(A, B\) and \(C\) \(\begin{array}{r} P(A \cup B \cup C)=P(A)+P(B)+P(C)-P(A) P(B) \ -P(A) P(C)-P(B) P(C)+P(A) P(B) P(C) \end{array}\) The correct option among the following isTS EAMCET 2020 Easy
- \(\theta\) and \(\alpha\) lie in \(Q_3\). If \(\cos (\theta-\alpha), \cos \theta, \cos (\theta+\alpha)\) are in harmonic progression, then \(\cos \theta \sec \frac{\alpha}{2}=\)TS EAMCET 2020 Medium
- is a complex cube root of unity. When an unbiased die is thrown times, if are the numbers appeared on the die, then the probability that and satisfy isTS EAMCET 2021 Easy
- The expansion of \((a+x)^n\) contains 15 terms. When \(x=1\) the ratio of the neighbouring terms to the middle term in this expansion is 16 . Then the positive integral value of ' \(a\) ' isTS EAMCET 2022 Easy
More PYQs from TS EAMCET
- The ratio of the displacements of a freely falling body during first, second and third seconds of its motion isTS EAMCET 2023 Medium
- If a function \(f(x)\) defined by \[ f(x)=\left\{\begin{array}{cc} a x+b, & x \leq-1 \ 2 x^2+2 b x-\frac{a}{2}, & -1 < x < 1 \text { is continuous } \ 7, & x \geq 1 \end{array}\right. \] on \(R\), then \((a, b)=\)TS EAMCET 2018 Easy
- If is the range of the ungrouped data then the absolute difference of the possible values of isTS EAMCET 2021 Easy
- A tetrahedron has vertices \(O(0,0,0), A(1,2,1)\), \(B(2,1,3), C(-1,1,2)\). If \(\theta\) is the angle between the faces \(O A B\) and \(A B C\), then \(\cos \theta=\)TS EAMCET 2020 Medium
- Two straight conducting rails form a right angle as shown below. A conducting bar in contact with the rails starts at the vertex at time and moves with constant velocity of along them. A magnetic field with is directed out of the page. The absolute value of the around the triangle at the time will be?
TS EAMCET 2020 Easy - balls are drawn one after the other without replacement from an urn containing red, blue and yellow balls. The probability of getting three different coloured balls isTS EAMCET 2022 Medium