Discussion Forum

If the straight lines $\frac{x-1}{2}=\frac{y+1}{K}=\frac{z}{2}$  and  $\frac{x+1}{5}=\frac{y+1}{2}=\frac{z}{k}$ are coplanar, then the plane (s) containing  these two lines is/are 

Answer:

Explanation:

Concept Involved If the straight lines are coplanar. They the should lie in same plane.
Description of Situation If straight lines are coplanar.

 $\Rightarrow$  $\begin{bmatrix}x_{2}-x_{1} & y_{2}-y_{1}&z_{2}-z_{1} \\a_{1} & b_{1}&c_{1}\\a_{2}& b_{2}&c_{2} \end{bmatrix}=0$

 Sol; Since  

$\frac{x-1}{2}=\frac{y+1}{K}=\frac{z}{2}$

 and  $\frac{x+1}{5}=\frac{y+1}{2}=\frac{z}{k}$ are coplanar,

 $\Rightarrow$   $\begin{bmatrix}2& 0&0 \\2 & K&2\\5&2&K \end{bmatrix}=0\Rightarrow K^{2}=4$

 $\Rightarrow$   $K=\pm 2$

 $\therefore$  $n_{1}=b_{1} \times d_{1}=6j-6k$ , for k=2