Question

Sketching Vectors Sketch representations of the given vector with initial points at $\text{(0,0),(2,3)}$and $\text{(-3,5)}$.

$\mathbf{u}=⟨0,-9⟩$.

Short answer

The representation of the given vector $\mathbf{u}=⟨0,-9⟩$ with initial point $(0,0),(2,3),(-3,5)$ is

Step-by-step solution

Step 1.Given information.

Initial points at$\text{(0,0),(2,3) ,(-3,5)}$

Vector $\mathbf{u}=⟨0,-9⟩$

Step 2. Terminal point and sketch the graph

For initial point find respective terminal point

Assume terminal point as $(x,y)$ substitute this in and rearrange to find terminal point.

Let the terminal point be$(x,y)$
When initial point at(0,0)

Vector $\mathbf{u}=⟨0,-9⟩$

$\begin{array}{l}v=〈x-x_1,y-y_1〉\\ ⟨0,-9⟩=⟨x-0,y-0⟩\\ x=0\\ y=-9\end{array}$

The terminal point is(0,-9)
When initial point is(2,3)

$\begin{array}{l}⟨0,-9⟩=⟨x-2,y-3⟩\\ x-2=0\\ x=2\\ y-3=-9\\ y=-9+3\\ y=-6\end{array}$

The terminal point is(2,-6)

when initial point is(-3,5)

$\begin{array}{l}⟨0,-9⟩=⟨x-(-3),y-5⟩\\ x+3=0\\ x=-3\\ y-5=-9\\ y=-9+5\\ y=-4\end{array}$

The terminal point is(-3,-4)

The representation of the u vector is