Chapter 9.4, Problem 45AYU

In Problems 43-48, find each quantity if $v=3i-5j\text{and}w=-2i+3j$.

$\Vert v\Vert -\Vert w\Vert$

To determine

To find: $\Vert v\Vert -\Vert w\Vert$

Answer to Problem 45AYU

Solution:

$\sqrt{34}-\sqrt{13}$

Explanation of Solution

Given:

$v=3i-5j$ and $w=-2i+3j$

Calculation:

Let $v=a_{1}i+b_{1}j=\langle a_1,b_1\rangle$. Then $\Vert v\Vert =\sqrt{a_1^2+b_1^2}$.

Here $a_1=3;b_1=-5$.

$\Vert v\Vert =\sqrt{{\left(3\right)}^2+{\left(-5\right)}^2}=\sqrt{9+25}=\sqrt{34}$

Here $a_1=-2;b_1=3$.

$\Vert w\Vert =\sqrt{{\left(-2\right)}^2+{\left(3\right)}^2}=\sqrt{4+9}=\sqrt{13}$

$\Vert v\Vert -\Vert w\Vert =\sqrt{34}-\sqrt{13}$