A) \[\sqrt{2}\]
B) \[\frac{5}{\sqrt{2}}\]
C) \[\frac{1}{\sqrt{2}}\]
D) 6
Correct Answer: A
Solution :
The slope of line \[x+y=1\] is \[-1\] \ It makes an angle of \[135{}^\circ \] with x-axis. The equation of line passing through \[(1,\,\,1)\] and making an angle of \[135{}^\circ \] is, \[\frac{x-1}{\cos {{135}^{o}}}=\frac{y-1}{\sin {{135}^{o}}}=r\] Þ \[\frac{x-1}{-1/\sqrt{2}}=\frac{y-1}{1/\sqrt{2}}=r\] Co-ordinates of any point on this line are \[\left( 1-\frac{r}{\sqrt{2}},1+\frac{r}{\sqrt{2}} \right)\]If this point lies on \[2x-3y=4\], then \[2\left( 1-\frac{r}{\sqrt{2}} \right)-3\left( 1+\frac{r}{\sqrt{2}} \right)=4\]Þ \[r=\sqrt{2}.\]
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