A) \[\frac{3}{2}\]
B) \[\frac{5}{2}\]
C) \[\frac{7}{2}\]
D) \[\frac{9}{2}\]
Correct Answer: D
Solution :
Idea If the lines \[\frac{x-{{x}_{1}}}{{{a}_{1}}}=\frac{y-{{y}_{1}}}{{{b}_{1}}}=\frac{z-{{z}_{1}}}{{{c}_{1}}}\] and \[\frac{x-{{x}_{2}}}{{{a}_{2}}}=\frac{y-{{y}_{2}}}{{{b}_{2}}}=\frac{z-{{z}_{2}}}{{{c}_{2}}}\]are coplanar, then \[\left| \begin{matrix} {{x}_{2}}-{{x}_{1}} & {{y}_{2}}-{{y}_{1}} & {{z}_{2}}-{{z}_{1}} \\ {{a}_{1}} & {{b}_{1}} & {{c}_{1}} \\ {{a}_{2}} & {{b}_{2}} & {{c}_{2}} \\ \end{matrix} \right|=0\] Here, for the given lines if the given lines are coplanar, then\[\left| \begin{matrix} 3-1 & k-1 & 0-1 \\ 2 & 3 & 4 \\ 1 & 2 & 1 \\ \end{matrix} \right|=0\] \[\Rightarrow \]\[-10+(k+1)2-1=0\]\[\Rightarrow \]\[k=9/2\] TEST Edge Equation of lines in various form related questions are asked. To solve such type of question, students are advised to understand the concept of line.
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