1.a) Find the position vector of P at t=3 s.

Here are the solutions to the problems:

1.a) Find the position vector of P at $t=3$ s.
The position vector of particle P is given by $\mathbf{r} = (t^2 - 2t)\mathbf{i} + (2t - 4)\mathbf{j}$ m.

Step 1: Substitute $t=3$ into the position vector equation.

$$\mathbf{r}(3) = ((3)^2 - 2(3))\mathbf{i} + (2(3) - 4)\mathbf{j}$$ $$\mathbf{r}(3) = (9 - 6)\mathbf{i} + (6 - 4)\mathbf{j}$$ $$$$