Medium INTEGER +4 / -1 PYQ · JEE Mains 2021

If the lines ${{x - k} \over 1} = {{y - 2} \over 2} = {{z - 3} \over 3}$ and
${{x + 1} \over 3} = {{y + 2} \over 2} = {{z + 3} \over 1}$ are co-planar, then the value of k is _____________.

Answer (integer) 1

Solution

$$\left| {\matrix{ {k + 1} &amp; 4 &amp; 6 \cr 1 &amp; 2 &amp; 3 \cr 3 &amp; 2 &amp; 1 \cr } } \right| = 0$$<br><br>$\Rightarrow$ $(k + 1)[2 - 6] - 4[1 - 9] + 6[2 - 6] = 0$<br><br>$\Rightarrow$ $k = 1$

About this question

Subject: Mathematics · Chapter: Three Dimensional Geometry · Topic: Direction Cosines and Ratios

This question is part of PrepWiser's free JEE Main question bank. 182 more solved questions on Three Dimensional Geometry are available — start with the harder ones if your accuracy is >70%.

Drill 25 more like these. Every day. Free.

PrepWiser turns these solved questions into a daily practice loop. Chapter-wise drills, full mocks, AI doubt chat. No auto-renew.

Start free →