Question

Help me solve this please:) I’ll give you brainliest

Answer 1

Step-by-step explanation:

Given:

$\vec{a} = 5\hat{\textbf{i}} + 4\hat{\textbf{j}}$

$\vec{b} = 5\hat{\textbf{i}} - 5\hat{\textbf{j}}$

Then

$2\vec{a} = 2(5\hat{\textbf{i}} + 4\hat{\textbf{j}})$

$\:\:\:\:\:\:= 10\hat{\textbf{i}} + 8\hat{\textbf{j}}$

$3\vec{b} = 3(5\hat{\textbf{i}} - 5\hat{\textbf{j}})$

$\:\:\:\:\:\:= 15\hat{\textbf{i}} - 15\hat{\textbf{j}}$

Therefore,

$2\vec{a} - 3\vec{b} = (10 - 15)\hat{\textbf{i}} + (8 - (-15))\hat{\textbf{j}}$

$= -5\hat{\textbf{i}} + 23\hat{\textbf{j}}$

To find the magnitude,

$|2\vec{a} - 3\vec{b}| = \sqrt{(-5)^2 + (23)^2}= 23.54$