\(\operatorname{Tan} \theta=\frac{m_{1}-m_{2}}{1+m_{1} m_{2}}\)
\(\mathrm{m}_{\mathrm{i}}=\) Gradient of any \(\mathrm{f}(\mathrm{x})\)
\(\mathrm{m}_{\mathrm{i}}=\frac{d y^{\prime}}{d x} ; \mathrm{y}=\mathrm{x}\)
\(=d y / d x=1\)
\(M_{1}=\frac{d y_{2}}{d x}=y_{2}=F x=3(x)^{1 / 2}\)
\(M=\frac{\sqrt{3}}{2} \times x^{-1 / 2}=\frac{\sqrt{3 / 2}}{\sqrt{x}}\)
Now at point of intersection,
\(Y_{1}=Y_{2}=x=\sqrt{3 x}\)
\(=\mathrm{x}^{2}=\mathrm{x}=\mathrm{x}(\mathrm{x}-1)=0\)
\(\therefore \mathrm{x}=0\) or \(\mathrm{x}=1\)
\(\mathrm{M}_{2}=\frac{\sqrt{3 / 2}}{\sqrt{1}}=\frac{\sqrt{3}}{2}\)
\(\operatorname{Tan} \theta=\frac{t-\sqrt{2 / 2}}{1+1 \times \sqrt{3} / 2}=\frac{0.2247}{2.2247}\)
\(\operatorname{Tan} \theta=-1, \tan ^{-1}(1)=45^{\circ}\)