Question

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

role="math" localid="1649603943715" $u=\left(3,6,11\right)andv=\left(1,-2,3\right)$

Short answer

The required value of$u+v=\left(4,4,14\right)andu-v=\left(2,8,8\right)$.

Step-by-step solution

Step 1. Given information. 

We have given vector$u=\left(3,6,11\right)andv=\left(1,-2,3\right)$

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

$$\begin{gathered} u+v=\left(x_1+x_2,y_1+y_2,z_1+z_2\right) \\ =\left(3+1,6+\left(-2\right),11+3\right) \\ =\left(4,4,14\right) \\ and \\ u-v=\left(x_1-x_2,y_1-y_2,z_1-z_2\right) \\ =\left(3-1,6-\left(-2\right),11-3\right) \\ =\left(2,8,8\right) \end{gathered}$$

Step 3. Sketch  u, v, u+v and u-v.

The graph of vector $u+v$.

The graph of vector $u-v$.