Question

Operations with Vectors Find,$2\mathbf{u},$ $-3\mathbf{v}$$,\mathbf{u}+\mathbf{v}$and $3\mathbf{u}-4\mathbf{v}$ for the given vectors $\mathbf{u}$ and $\mathbf{v}$.

$\mathbf{u}=\mathbf{i},\mathbf{v}=-2\mathbf{j}$.

Short answer

For

$\begin{array}{l}u=i\\ v=-2j\end{array}$

$\begin{array}{l}2u=2i\\ -3v=6j\\ u+v=i-2j\\ 3u-4v=3i+8j\end{array}$

Step-by-step solution

Step 1.Given information.

Given:

$\begin{array}{l}u=i\\ v=-2j\end{array}$

Step 2. To find:  2u,−3v,u+v,3u−4v.

Use vector algebric operations accordingly to get the value for each condition

$\begin{array}{l}-3v=6j\\ 2u=2i\\ -3v=-3(-2j)\\ -3v=6j\\ u+v=i-2j\\ 3u-4v=3i-4(-2j)\\ 3u-4v=3i+8j\end{array}$