Q 23. - Calculus

Question

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

$u=\left(2,-6\right), v=\left(6, 2\right)$,

Step-by-Step Solution

Answer

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

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   a n d     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 

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

Step 3. Sketch u ,   v ,   u + v and u - v .

The graph of vector $u+v$.

The graph of vector $u-v$.