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 $\mathbf{v}$.

$\mathbf{u}=⟨2,7⟩,\mathbf{v}=⟨3,1⟩$.

Short answer

For

$\begin{array}{l}u=⟨-2,5⟩\\ v=⟨2,-8⟩\end{array}$

$\begin{array}{l}2u=⟨-4,10⟩\\ -3v=⟨-6,24⟩\\ u+v=⟨0,-3⟩\\ 3u-4v=⟨-14,47⟩\end{array}$

Step-by-step solution

Step 1.Given information.

Given:$\begin{array}{l}u=⟨-2,5⟩\\ v=⟨2,-8⟩\end{array}$

Step 2. To find:  2u,−3v,u+v,3u−4v

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

$\begin{array}{l}2u=2⟨-2,5⟩\\ 2u=⟨-4,10⟩\\ -3v=-3⟨2,-8⟩\\ -3v=⟨-6,24⟩\end{array}$

$\begin{array}{l}u+v=⟨-2,5⟩+⟨2,-8⟩\\ =⟨-2+2,5-8⟩\\ u+v=⟨0,-3⟩\\ 3u-4v=3⟨-2,5⟩-4⟨2,-8⟩\\ =⟨-6,15⟩-⟨8,-32⟩\\ =⟨-6-8,15-(-32)⟩\\ 3u-4v=⟨-14,47⟩\end{array}$