Question

Find $u+vandu-v$also sketch $u,v,u+v,u-v$

role="math" localid="1649595165778" $u=\left(1,-2\right)andv=\left(-3,6\right)$

Short answer

The required value of$\left(u+v\right)=\left(-2,4\right)and\left(u-v\right)=\left(4,-8\right)$.

Step-by-step solution

Step 1. Given information. 

We have given vector$u=\left(1,-2\right)andv=\left(-3,6\right)$

Step 2. Find the values of u+v and u-v.

$$\begin{gathered} u+v=\left(x_1+x_2,y_1+y_2\right) \\ =\left(1+\left(-3\right),-2+6\right) \\ =\left(1-3,-2+6\right) \\ =\left(-2,4\right) \end{gathered}$$

and

$$\begin{gathered} u-v=\left(x_1-x_2,y_1-y_2\right) \\ =\left(1-\left(-3\right),-2-6\right) \\ =\left(1+3,-2-6\right) \\ =\left(4,-8\right) \end{gathered}$$

Step 3. Sketch u , v u+v and u-v

The graph of vector $u+v$.

The graph of vector $u-v$.