Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
If a plane passing through the points $(2,3,0),(0,-5,2)$ and $(-2,0,3)$ meets the $\mathrm{X}, \mathrm{Y}, \mathrm{Z}$-axes in $\mathrm{A}, \mathrm{B}, \mathrm{C}$ respectively then $\mathrm{A}=$
MathematicsThree Dimensional GeometryTS EAMCETTS EAMCET 2022 (20 Jul Shift 1)
Options:
  • A $\left(\frac{3}{7}, 0,0\right)$
  • B $\left(\frac{7}{3}, 0,0\right)$
  • C $\left(\frac{21}{13}, 0,0\right)$
  • D $(21,0,0)$
Solution:
2065 Upvotes Verified Answer
The correct answer is: $\left(\frac{7}{3}, 0,0\right)$
Given points from which plane passing through are $(2,3,0),(0,-5,2)$ and $(-2,0,3)$.
Let the equation of plane be $\frac{\mathrm{x}}{\mathrm{a}}+\frac{\mathrm{y}}{\mathrm{b}}+\frac{\mathrm{z}}{\mathrm{c}}=1$. Satisfy all the points,


$\frac{2}{a}+\frac{3}{b}=1$

Multiply equation (ii) by 3 and (iv) by 5 and then add,
$$
\begin{gathered}
\frac{-15}{b}+\frac{16}{c}=3 \\
\frac{\frac{15}{b}+\frac{15}{c}=10}{\frac{21}{c}=13}
\end{gathered}
$$
From (iii)
$$
\begin{aligned}
& \frac{-2}{\mathrm{a}}+\frac{3 \times 13}{21}=1 \\
& \Rightarrow \frac{13}{7}-1=\frac{2}{\mathrm{a}} \Rightarrow \mathrm{a}=\frac{7}{3}
\end{aligned}
$$
So, intercept of $\mathrm{A}$ is $(7 / 3,0,0)$

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.