Question

The three lines drawn from O with direction ratios, (1, –1, k), (2, –3, 0) and (1, 0, 3) are coplanar. Then k =

• A. 1
• B. no such k exists
• C. 7

Answer 1

The correct option is A 1

If lines are coplanar and l, m, n are d.c.’s of the normal to the plane, then
l – 1.m + k.n = 0
l – 3.m + 0.n = 0
l – 0.m + 3.n = 0
$\Rightarrow \left|\begin{array}{ccc}1& -1& k\\ 2& -3& 0\\ 1& 0& 3\end{array}\right|=0\Rightarrow k=1$