Question

Find $u+v$and $u-v$. Also, sketch $u,v,u+v$and $u-v$.

role="math" localid="1649572653771" $u=\left(2,-6\right),v=\left(6,2\right)$,

Short answer

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

Step-by-step solution

Step 1. Given information.  

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

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

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

and

localid="1649577561095" $$\begin{gathered} \left(u-v\right)=\left(x_1-x_2,y_{{}_1}-y_2\right) \\ =\left(2-6,-6-2\right) \\ =\left(-4,-8\right) \end{gathered}$$

Step 3. Sketchu, v, u+vand u-v.

The graph of vector$u+v$.

The graph of vector $u-v$.