A) Two values of \[a\]
B) \[\forall a\]
C) For one value of \[a\]
D) For no value of \[a\]
Correct Answer: A
Solution :
\[\because \] The lines are perpendicular, if coefficient of \[{{x}^{2}}\] + coefficient of \[{{y}^{2}}=0\] Þ \[3a+({{a}^{2}}-2)=0\] Þ \[{{a}^{2}}+3a-2=0\] \[\because \] The equation is a quadratic equation in ?a? and \[{{B}^{2}}-4AC>0\]. \ The roots of a are real and distinct. Therefore, the lines are perpendicular to each other for two values of ?a?.
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