Answer
$x(t) = 3t^2, \quad y(t) = -2$
Work Step by Step
Step 1
Given: \[ \mathbf{r}(t) = 3t^2\mathbf{i} - 2\mathbf{j} \]
Step 2
Since the vector equation of the curve given by: \[ \mathbf{r}(t) = x(t)\mathbf{i} + y(t)\mathbf{j} \] is: \[ \mathbf{r}(t) = 3t^2\mathbf{i} - 2\mathbf{j} \] then the corresponding parametric equations to the given vector equation are: \[ x(t) = 3t^2, \quad y(t) = -2 \] Result \[ x(t) = 3t^2, \quad y(t) = -2 \]
