Answer
The line passing through the point $(3,0)$ and parallel to the vector $(-2\mathbf{i} + 5\mathbf{j})$
Work Step by Step
Step 1
Given the vector equation below: \[ \mathbf{r}(t) = (3 -2t)\mathbf{i} + 5\mathbf{j}t \] and using the standard form of the vector equation below: \[ \mathbf{r}(t) = x(t)\mathbf{i} + y(t)\mathbf{j} \] compare the two functions together: \[ x(t)\mathbf{i} + y(t)\mathbf{j} = (3 - 2t)\mathbf{i} + 5t\mathbf{j} \] So, the parametric equations are: \[ x(t) = 3 - 2t, \quad y(t) = 5t \]
Step 2
As a result, the graph of the equation represents the line in 2-dimensional space passing through the point $(3,0)$ and parallel to the vector $(-2\mathbf{i} + 5\mathbf{j})$.
