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 the points $(1,2,3)$ and $(2,-1,0)$ lie on the opposite sides of the plane $2 x+3 y-2 z=k$, then
MathematicsThree Dimensional GeometryVITEEEVITEEE 2014
Options:
  • A $k < 1$
  • B $k>2$
  • C $k < 1$ or $k>2$
  • D $1 < k < 2$
Solution:
2304 Upvotes Verified Answer
The correct answer is: $1 < k < 2$
The points $(1,2,3)$ and $(2,-1,0)$ lie on the opposite sides of the plane $2 x+3 y-2 z-k=0$
So, $(2+6-6-\mathrm{k})(4-3-\mathrm{k}) < 0$
$\begin{array}{l}
\Rightarrow(\mathrm{k}-1)(\mathrm{k}-2) < 0 \\
\therefore 1 < \mathrm{k} < 2
\end{array}$

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.