WBJEE · Maths · Three Dimensional Geometry
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 & Solution
Correct Answer
(B) coplanar
Step-by-step Solution
Detailed explanation
\(\quad\) \(\Delta=\left|\begin{array}{ccc}1 & -1 & 1 \\ 2 & -3 & 0 \\ 1 & 0 & 3\end{array}\right|\) \(=1(-9-0)-(-1) \cdot(6-0)+1(0-(-3))\) \(=-9+6+3=0\) since, \(\Delta=0\) \(\therefore\) Lines are coplanar.
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