Question

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

$\mathbf{u}=⟨-7,2⟩$

Short answer

The representation of the given vector $\mathbf{u}=⟨-7,2⟩$ with initial points (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 $\mathbf{u}=⟨-7,2⟩$

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 $\mathbf{u}=⟨-7,2⟩$

$\begin{array}{l}v=〈x-x_1,y-y_1〉\\ ⟨-7,2⟩=⟨x-0,y-0⟩\\ x-0=-7\\ x=-7\\ y-0=2\\ y=2\end{array}$

The terminal point is(-7,2)
When initial point is(2,3)

$\begin{array}{l}⟨-7,2⟩=⟨x-2,y-3⟩\\ x-2=-7\\ x=-5\\ y-3=2\\ y=5\end{array}$

The terminal point when initial point(2,3) is(-5,5)

When initial point at(-3,5)

$\begin{array}{l}⟨-7,2⟩=⟨x-(-3),y-5⟩\\ x+3=-7\\ x=-7-3\\ x=-10\\ y-5=2\\ y=7\end{array}$

The terminal point when initial point (-3,5) is(-10,7)

The representation of the vector u is,