A) any value
B) exactly one value
C) exactly two values
D) exactly three values
Correct Answer: C
Solution :
Lines are co−planer\[\Rightarrow S.\text{ }D.=0\] \[\Rightarrow \]\[\left| \begin{matrix} 2-1 & 3-4 & 4-5 \\ 1 & 1 & -k \\ k & 2 & 1 \\ \end{matrix} \right|=0\] \[\Rightarrow \]\[\left| \begin{matrix} 1 & -1 & -1 \\ 1 & 1 & -k \\ k & 2 & 1 \\ \end{matrix} \right|=0\] \[(1+2k)+(1+{{k}^{2}})-(2-k)=0\] \[3k+{{k}^{2}}=0\] \[k(k+3)=0\] k = 0 or k = −3 Exactly two values.
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