$$\mathrm{a}$$ and $$\mathrm{b}$$ are the intercepts made by a line on the co-ordinate axes. If $$3 \mathrm{a}=\mathrm{b}$$ and the line passes through $$(1,3)$$, then the equation of the line is

Let $$\bar{a}, \bar{b}$$ and $$\bar{c}$$ be three unit vectors such that $$\bar{a} \times(\bar{b} \times \bar{c})=\frac{\sqrt{3}}{2}(\bar{b}+\bar{c})$$. If $$\bar{b}$$ is not parallel to $$\bar{c}$$, then the angle between $$\bar{a}$$ and $$\bar{b}$$ is

The vector equation of the line $$2 x+4=3 y+1=6 z-3$$ is

If $$\overline{\mathrm{a}}$$ and $$\overline{\mathrm{b}}$$ are two unit vectors such that $$\overline{\mathrm{a}}+2 \overline{\mathrm{b}}$$ and $$5 \bar{a}-4 \bar{b}$$ are perpendicular to each other, then the angle between $$\bar{a}$$ and $$\bar{b}$$ is