Q 24. - Calculus

Question

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

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

Step-by-Step Solution

Answer

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

Step 1. Given information.

We have given vector 

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

Step 2. Find the values of u + v   a n d   u - v .

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

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 $u-v$.