Step-by-step explanation:
Given:
[tex]\vec{a} = 5\hat{\textbf{i}} + 4\hat{\textbf{j}}[/tex]
[tex]\vec{b} = 5\hat{\textbf{i}} - 5\hat{\textbf{j}}[/tex]
Then
[tex]2\vec{a} = 2(5\hat{\textbf{i}} + 4\hat{\textbf{j}})[/tex]
[tex]\:\:\:\:\:\:= 10\hat{\textbf{i}} + 8\hat{\textbf{j}}[/tex]
[tex]3\vec{b} = 3(5\hat{\textbf{i}} - 5\hat{\textbf{j}})[/tex]
[tex]\:\:\:\:\:\:= 15\hat{\textbf{i}} - 15\hat{\textbf{j}}[/tex]
Therefore,
[tex]2\vec{a} - 3\vec{b} = (10 - 15)\hat{\textbf{i}} + (8 - (-15))\hat{\textbf{j}}[/tex]
[tex]= -5\hat{\textbf{i}} + 23\hat{\textbf{j}}[/tex]
To find the magnitude,
[tex]|2\vec{a} - 3\vec{b}| = \sqrt{(-5)^2 + (23)^2}= 23.54[/tex]
