Q 27. - Calculus

Question

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

$u=\left(1,-4, 6\right) and v=\left(2,-4, 7\right)$

Step-by-Step Solution

Answer

The required value of $u+v=\left(3, -8, 13\right) and u-v=\left(-1, 0, -1\right)$.

Step 1. Given information.

We have given vector $u=\left(1,-4, 6\right) and v=\left(2,-4, 7\right)$.

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

$$\begin{gathered} u+v=\left(x_1+x_2, y_1+y_2, z_1+z_2\right) \\ =\left(1+2,-4+\left(-4\right),6+7\right) \\ =\left(3,-8,13\right) \\ and \\ u-v=\left(x_1-x_2, y_1-y_2, z_1-z_2\right) \\ =\left(1-2,-4-\left(-4\right),6-7\right) \\ =\left(-1,0, -1\right) \end{gathered}$$

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

The graph of vector $u+v$.

The graph of vector $u-v$.