Notes: `u = -21i` Use the dot product to find the magnitude of u.

Sunday, 11 December 2016

$\displaystyle{u}=-{21}{i}$ Use the dot product to find the magnitude of u.

The magnitude of a vector $\displaystyle{u}$ is the square root of its dot product by itself, because

$\displaystyle{u}\cdot{u}={\left|{\left|{u}\right|}\right|}\cdot{\left|{\left|{u}\right|}\right|}\cdot{\cos{{\left(\theta\right)}}},$ and $\displaystyle\theta={0},$ $\displaystyle{\cos{{\left(\theta\right)}}}={1}.$

I suppose that the magnitude of $\displaystyle{i}$ is 1. Then

$\displaystyle{\left|{\left|{u}\right|}\right|}=\sqrt{{{u}\cdot{u}}}=\sqrt{{{\left(-{21}{i}\right)}\cdot{\left(-{21}{i}\right)}}}=\sqrt{{{21}\cdot{21}}}={21}.$

This is the answer.

The magnitude of a vector $\displaystyle{u}$ is the square root of its dot product by itself, because

I suppose that the magnitude of $\displaystyle{i}$ is 1. Then

$\displaystyle{\left|{\left|{u}\right|}\right|}=\sqrt{{{u}\cdot{u}}}=\sqrt{{{\left(-{21}{i}\right)}\cdot{\left(-{21}{i}\right)}}}=\sqrt{{{21}\cdot{21}}}={21}.$

This is the answer.