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True [87]
3 years ago
11

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

Mathematics
1 answer:
mash [69]3 years ago
6 0

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

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