Question

Three lines are drawn from the origin $O$ with direction cosines proportional to $(1,-1,1),(2-3,0)$ and $(1,0,3)$. The three lines are

• A. Not coplanar
• B. Coplanar
• C. Perpendicular to each other
• D. Coincident

Answer 1

The correct option is B Coplanar

The lines are drawn from origin $O$ with d.cs proportional to $(1,-1,1),(2,-3,0)$ and $(1,0,3)$

Consider, $\left|\begin{array}{ccc}1& -1& 1\\ 2& -3& 0\\ 1& 0& 3\end{array}\right|$

$=1(-9-0)+1(6-0)+1(0+3)$

$=-9+9=0$

$\therefore \Delta =0$

Hence, the lines are co-planar.