Question

use the vectors $v=-2i+j$and $w=4i-3j$to find:

$\parallel v\parallel +\parallel w\parallel$

Short answer

$\parallel v\parallel +\parallel w\parallel =5+\sqrt{5}$

Step-by-step solution

Step 1. Given information

We have to find the value of $\parallel v\parallel +\parallel w\parallel$using :

role="math" $$\begin{gathered} v=-2i+j \\ w=4i-3j \end{gathered}$$

Step 2. Find the value

We know that the magnitude of the vector is given by :

$\parallel v\parallel =\sqrt{{a_1}^2+{b_1}^2}$

Apply it for the given equation :

localid="1646892047521" $$\begin{gathered} \parallel v\parallel +\parallel w\parallel =\sqrt{{(-2)}^2+{\left(1\right)}^2}+\sqrt{{\left(4\right)}^2+{(-3)}^2} \\ \parallel v\parallel +\parallel w\parallel =\sqrt{4+1}+\sqrt{16+9} \\ \parallel v\parallel +\parallel w\parallel =\sqrt{5}+\sqrt{25} \\ \parallel v\parallel +\parallel w\parallel =5+\sqrt{5} \end{gathered}$$