Magnitude of a Vector Formula

Magnitude is the length of a vector and is denoted by |v|. Magnitude of a vector is always a positive number or zero it cannot be a negative number.

Formula of Magnitude of a Vector

Magnitude of a vector when end point is origin. Let x and y are the components of the vector,

\[\large \left|v\right|=\sqrt{x^{2}+y^{2}}\]

Magnitude of a vector when starting points are $(x_{1}$, $y_{1})$ end points are  $(x_{2}$, $y_{2})$,

\[\large \left|v\right|=\sqrt{\left(x_{2}+x_{1}\right)^{2}+\left(y_{2}+y_{1}\right)^{2}}\]

solved examples

Question: Find the magnitude of the vector with $\vec{u}$ = (3,5) ?


Given, $\vec{u}$ = (3,5)

Use magnitude formula,

$|v|$ = $\sqrt{x^{2}+y^{2}}$

$|v|$ = $\sqrt{3^{2}+5^{2}}$

$|v|$ = $\sqrt{9 + 25}$

$|v|$ = 5.83


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