• # question_answer If the lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$and $\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}$are coplanar. then k is equal to A)  $\frac{3}{2}$                                   B)  $\frac{5}{2}$ C)  $\frac{7}{2}$                                   D)  $\frac{9}{2}$

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.