Question
Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~1,~-4\right) $ .
Answer
The magnitude of vector $ \vec{v} $ is $ \| \vec{v} \| = \sqrt{ 21 } $ .
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 = 2 $ , $ b = 1 $ and $ c = -4 $ so:
$$ ||v|| = \sqrt{ 2^2 + 1^2 + (-4)^2} = \sqrt{ 4 + 1 + 16} = \sqrt{ 21 } = \sqrt{ 21 }$$This page was created using
Vectors Calculator