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 $\mathbf{v}$.

$\mathbf{u}=⟨0,-1⟩,\mathbf{v}=⟨-2,0⟩$.

Short answer

For

$\begin{array}{l}u=⟨0,-1⟩\\ v=⟨-2,0⟩\end{array}$

$\begin{array}{l}2u=⟨0,-2⟩\\ -3v=⟨6,0⟩\\ u+v=⟨-2,-1⟩\\ 3u-4v=⟨8,-3⟩\end{array}$

Step-by-step solution

Step 1.Given information.

Given:

$\begin{array}{l}u=⟨0,-1⟩\\ v=⟨-2,0⟩\end{array}$

Step 2. To find:  2u,−3v,u+v,3u−4v.

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

$\begin{array}{l}u+v=⟨-2,-1⟩\\ 3u-4v=⟨8,-3⟩\\ 2u=2⟨0,-1⟩\\ 2u=⟨0,-2⟩\\ -3v=-3⟨-2,0⟩\\ -3v=⟨6,0⟩\end{array}$

$\begin{array}{l}u+v=⟨0,-1⟩+⟨-2,0⟩\\ =⟨0-2,-1+0⟩\\ u+v=⟨-2,-1⟩\\ 3u-4v=3⟨0,-1⟩-4⟨-2,0⟩\\ =⟨0,-3⟩-⟨-8,0⟩\\ =⟨0-(-8),-3-0⟩\\ 3u-4v=⟨8,-3⟩\end{array}$