Question

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

$u=⟨4,-6⟩$.

Short answer

The representation of the given vector 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 $u=⟨4,-6⟩$

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 $u=⟨4,-6⟩$

$\begin{array}{l}v=〈x-x_1,y-y_1〉\\ ⟨4,-6⟩=⟨x-0,y-0⟩\\ x=4\\ y=-6\end{array}$

The terminal point is(4,-6)
When initial point is(2,3)

$\begin{array}{l}⟨4,-6⟩=⟨x-2,y-3⟩\\ x-2=4\\ x=6\\ y-3=-6\\ y=-6+3\\ y=-3\end{array}$

The terminal point when initial point is(2,3) is(6,-3)

When initial point is(-3,5)

$\begin{array}{l}⟨4,-6⟩=⟨x-(-3),y-5⟩\\ ⟨4,-6⟩=⟨x+3,y-5⟩\\ x+3=4\\ x=1\\ y-5=-6\\ y=-6+5\\ y=-1\end{array}$

The terminal point when initial point is(-3,5)is(1,-1)

The representation of the vector u is