Q 25. - Calculus

Question

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

$u=\left(1,-2\right) and v=\left(-3, 6\right)$

Step-by-Step Solution

Answer

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

Step 1. Given information.

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

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