Question

In Problems $45$, find each quantity if v = $3i-5j$and w = $-2i+3j$.

$45$. |v| - |w|

Short answer

Answer is 2.22

Step-by-step solution

- Given information

V = 3i-5j and W = -2i+3j

- To find

1. Mod of V

2. Mod of W

3. Substract mod of W from mod of V.

- Solution part 1

$$\begin{gathered} \left|V\right|=\left|3i-5j\right| \\ =\sqrt{\left(3^2\right)+\left(5^2\right)} \\ =\sqrt{\left(9\right)+\left(25\right)} \\ =\sqrt{\left(34\right)} \\ =5.83 \end{gathered}$$

- Solution part 2

$$\begin{gathered} \left|W\right|=\left|-2i+3j\right| \\ =\sqrt{\left(2^2\right)+\left(3^2\right)} \\ =\sqrt{\left(4\right)+\left(9\right)} \\ =\sqrt{13} \\ =3.60 \end{gathered}$$

- Solution part 3

$\left|V\right|-\left|W\right|=5.83-3.60=2.22$