Question

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

role="math" localid="1649578020551" $u=\left(3,-4\right)andv=\left(-1,5\right)$

Short answer

The required value is$\left(u+v\right)=\left(2,1\right)and\left(u-v\right)=\left(4,-9\right)$.

Step-by-step solution

Step 1. Given information.  

We have given vector

$u=\left(3,-4\right)andv=\left(-1,5\right)$

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

$$\begin{gathered} \left(u+v\right)=\left(x_1+x_2,y_1+y_2\right) \\ =\left(3+\left(-1\right),-4+5\right) \\ =\left(3-1,-4+5\right) \\ =\left(2,1\right) \end{gathered}$$

and

$$\begin{gathered} \left(u-v\right)=\left(x_1-x_2,y_1-y_2\right) \\ =\left(3-\left(-1\right),-4-5\right) \\ =\left(3+1,-4-5\right) \\ =\left(4,-9\right) \end{gathered}$$

Step 3. Sketch u,v, u+v and u-v.

The graph of vector$u+v$.

The graph of vector $u-v$.