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
The two lines $x=a y+b, z=c y+d$ and $x=a^{\prime} y+b^{\prime} z=c^{\prime} y+d^{\prime}$ will be perpendicular, if and only if
MathematicsThree Dimensional GeometryJEE MainJEE Main 2003
Options:
  • A
    $a a^{\prime}+c c^{\prime}+1=0$
  • B
    $\mathrm{a} \mathrm{a}^{\prime}+\mathrm{b} \mathrm{b}^{\prime}+\mathrm{c} \mathrm{c}^{\prime}+1=0$
  • C
    $\mathrm{a}^{\prime}+\mathrm{b} \mathrm{b}^{\prime}+\mathrm{c} \mathrm{c}^{\prime}=0$
  • D
    $\left(a+a^{\prime}\right)\left(b+b^{\prime}\right)+\left(c+c^{\prime}\right)=0$
Solution:
2929 Upvotes Verified Answer
The correct answer is:
$a a^{\prime}+c c^{\prime}+1=0$
$\frac{\mathrm{x}-\mathrm{b}}{\mathrm{a}}=\frac{\mathrm{y}}{1}=\frac{3-\mathrm{d}}{\mathrm{c}} ; \frac{\mathrm{x}-\mathrm{b}^{\prime}}{\mathrm{a}^{\prime}}=\frac{\mathrm{y}}{1}=\frac{3-\mathrm{d}^{\prime}}{\mathrm{c}^{\prime}}$
For perpendicular $\mathrm{aa}^{\prime}+1+\mathrm{cc}^{\prime}=0$

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.