Q 28. - Calculus

Question

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

$u=\left(3,6,11\right) and v=\left(1,-2, 3\right)$

Step-by-Step Solution

Answer

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

Step 1. Given information.

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

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

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

Step 3. Sketch u ,   v ,   u + v   a n d   u - v .

The graph of vector $u+v$.

The graph of vector $u-v$.