A) \[\frac{10}{3}\]
B) \[\frac{-8}{3}\]
C) \[\frac{-10}{3}\]
D) \[\frac{8}{3}\]
Correct Answer: C
Solution :
Here, \[{{g}_{1}}=\frac{k}{2},\,{{f}_{1}}=2,\,{{c}_{1}}=2\] \[{{g}_{2}}=-1,\,{{f}_{2}}=\frac{-3}{4},\,{{c}_{2}}=\frac{k}{2}\] Condition for orthogonal intersection, Þ \[2({{g}_{1}}{{g}_{2}}+{{f}_{1}}{{f}_{2}})={{c}_{1}}+{{c}_{2}}\] Þ \[2\,\left[ \frac{-k}{2}+\left( \frac{-3}{2} \right) \right]=2+\frac{k}{2}\] Þ \[-k-3=2+\frac{k}{2}\] Þ \[\frac{3k}{2}=-5\]; \[k=\frac{-10}{3}\].
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