InterviewSolution
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InterviewSolution
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Two straight paths are represented by the equations ` x - 3y = 2` and `-2x + 6y = 5`. Check whether the paths cross each other or not. |
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Answer» Given linear equations are `x-3y-2=0 " " ...(i)` and `-2x+6y-5=0" " ...(ii)` On comparing both the equations with `ax+by+c=0`, we get `a_(1)=1,b_(1)=-3` and `c_(1)=-2" " `[from Eq.(i)] `a_(2)=-2,b_(2)=6` and `c_(2)=-5" " `[from Eq.(ii)] Here, `" " (a_(1))/(a_(2))=(1)/(-2)` `(b_(1))/(b_(2))=(-3)/(6)=-(1)/(2)` and `(c_(1))/(c_(2))=(-2)/(-5)=(2)/(5)` i.e., `" " (a_(1))/(a_(2))=(b_(1))/(b_(2))!=(c_(1))/(c_(2))" "` [parallel lines] Hence, two straight paths represented by the given equation never cross each other, because they are parallel to each other. |
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