WeBWorK Standalone Renderer

The figure below shows a named point $P$ and a vector $\mathbf{v}$ in $\mathbb{R}^2$ .

Part 1

Find the coordinate vector for .
- $\mathbf{v}=$

Find and draw the vector for the following values of .
- When $t = -2$ , $t \mathbf{v} =$
- When $t = -1$ , $t \mathbf{v} =$
- When $t = 0$ , $t \mathbf{v} =$
- When $t = 1$ , $t \mathbf{v} =$
- When $t = 2$ , $t \mathbf{v} =$

As $t$ increases, the tips of the position vectors $t \mathbf{v}$ trace the from because and from because .

Part 2

Find the coordinates of the point .
- $P =$

Find and draw the vector for the following values of .
- When $t = -2$ , $P + t \mathbf{v} =$
- When $t = -1$ , $P + t \mathbf{v} =$
- When $t = 0$ , $P + t \mathbf{v} =$
- When $t = 1$ , $P + t \mathbf{v} =$
- When $t = 2$ , $P + t \mathbf{v} =$

As $t$ increases, the tips of the position vectors $P + t \mathbf{v}$ trace the from because and from because . Notice that the set of points traced out by $t \mathbf{v}$ is to the set of points traced out by $P + t \mathbf{v}$ .

You can earn partial credit on this problem.