If the lines x+12=y-11=z+13 and x+22=y-k3= z4 are coplanar, then the value of k is:

Question

If the lines $\dfrac{x+1}2=\dfrac{y-1}1=\dfrac{z+1}3$ and $\dfrac{x+2}2=\dfrac{y-k}3=\dfrac z4$ are coplanar, then the value of $k$ is:

Accepted Answer

$$\begin{vmatrix}-1&k-1&1\2&1&3\2&3&4\end{vmatrix}=0\implies -1(4-9)-(k-1)(8-6)+(6-2)=0\implies 5-2(k-1)+4=0\implies k=\frac{11}2.$$

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