Question
Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 1 }{ 2 },~\sqrt{ 3 },~5\right) $ .
Answer
The magnitude of vector $ \vec{v} $ is $ \| \vec{v} \| = \dfrac{\sqrt{ 113 }}{ 2 } $ .
Explanation
To find magnitude of a vector $ v=(a,b,c) $ we use formula $ ||v|| = \sqrt{a^2+b^2+c^2} $
In this example $ a = \frac{ 1 }{ 2 } $ , $ b = \sqrt{ 3 } $ and $ c = 5 $ so:
$$ ||v|| = \sqrt{ \left(\frac{ 1 }{ 2 }\right)^2 + \left( \sqrt{ 3 } \right)^{ 2 } + 5^2} = \sqrt{ \frac{ 1 }{ 4 } + 3 + 25} = \sqrt{ \frac{ 113 }{ 4 } } = \frac{\sqrt{ 113 }}{ 2 }$$This page was created using
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