Question

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

$u=⟨3,5⟩$.

Short answer

The representation of the given vector with initial points $\text{(0,0),(2,3) ,(-3,5)}$ is.

Step-by-step solution

Step 1.Given information.

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

Vector$u=⟨3,5⟩$

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 $u=(3,5)$

$\begin{array}{l}v=〈x-x_1,y-y_1〉\\ ⟨3,5⟩=⟨x-0,y-0⟩\\ x=3\\ y=5\end{array}$

The terminal point is$(3,5)$
When initial point is$(2,3)$

$\begin{array}{l}⟨3,5⟩=⟨x-2,y-3⟩\\ x-2=3\\ x=3+2\\ x=5\\ y-3=5\\ y=8\end{array}$

The terminal point$(5,8)$.

When initial point is $(-3,5)$,

$\begin{array}{l}⟨3,5⟩=⟨x-(-3),y-5⟩\\ x+3=3\\ x=0\\ y-5=5\\ y=10\end{array}$

The terminal point is(0,10)

The representation of the $u$ vector is