If $$[\vec{a}\ \vec{b}\ \vec{c}\ ] \neq 0$$, then $$\frac{[\vec{a}\ +\vec{b}\ \vec{b}\ +\vec{c}\ \vec{c}\ +\vec{a}\ ]}{[\vec{b}\ \vec{c}\ \vec{a}\ ]}=$$

The cartesian co-ordinates of the point on the parabola $$y^2=x$$ whose parameter is $$-\frac{4}{3}$$ are

The angle between the line $$r =(\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}})+\lambda(3 \hat{\mathbf{i}}+\hat{\mathbf{j}})$$ and the plane $$\mathbf{r} \cdot(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})=8$$ is

The bacteria increases at the rate proportional to the number of bacteria present. If the original number '$$N$$' doubles in $$4 \mathrm{~h}$$, then the number of bacteria in $$12 \mathrm{~h}$$ will be