• the coordinates of a point which is at a distance of 1/root2 units from (1,1) in the direction of line x + y - 3= 0
• answer is (1/2, 3/2)

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{We} \mathrm{have} \\ \mathrm{x}+\mathrm{y}-3=0 \\ \mathrm{tan\theta }=-1 \\ \mathrm{Hence} \\ \mathrm{\theta }=135° \\ \mathrm{cos\theta }=-\frac{1}{\sqrt{2}} \\ \mathrm{sin\theta }=\frac{1}{\sqrt{2}} \\ \mathrm{Using} \mathrm{parametric} \mathrm{form} \mathrm{of} \mathrm{line} \mathrm{we} \mathrm{get} \\ \left(\mathrm{x},\mathrm{y}\right)=\left(1+\frac{1}{\sqrt{2}}\mathrm{cos\theta },1+\frac{1}{\sqrt{2}}\mathrm{sin\theta }\right) \\ =\left(1-\frac{1}{\sqrt{2}}\frac{1}{\sqrt{2}}+1+\frac{1}{\sqrt{2}}\frac{1}{\sqrt{2}}\right) \\ =\left(1-\frac{1}{2},1+\frac{1}{2}\right) \\ =\left(\frac{1}{2},\frac{3}{2}\right) \left[\mathrm{Answer}\right] \end{gathered}$$

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