Painevg

2021-12-17

Dot product of a vector with itself Calculate ${V}_{1}\cdot {V}_{1}$. Express your answer in terms of ${V}_{1}$.
${V}_{1}\cdot {V}_{1}=$

Lynne Trussell

Expert

The dot product of wo vectors ${\stackrel{\to }{V}}_{1}$ and ${\stackrel{\to }{V}}_{1}$ is,
${\stackrel{\to }{V}}_{1}\cdot {\stackrel{\to }{V}}_{1}=|{\stackrel{\to }{V}}_{1}||{\stackrel{\to }{V}}_{1}|{\mathrm{cos}0}^{\circ }$
$={V}_{1}^{2}$
The dot product of single vector with itself is the square of magnitude of the vector.

Mollie Nash

Expert

nick1337

Expert

Dot product of a vector with itself :
${\stackrel{\to }{V}}_{1}\cdot {\stackrel{\to }{V}}_{1}=|{\stackrel{\to }{V}}_{1}||{\stackrel{\to }{V}}_{1}|\mathrm{cos}\left(\theta \right)$
But  $\theta =0$. (Angle between same vector.)
$\therefore {\stackrel{\to }{V}}_{1}\cdot {\stackrel{\to }{V}}_{1}=|{\stackrel{\to }{V}}_{1}||{\stackrel{\to }{V}}_{1}|\mathrm{cos}\left(0\right)$
$⇒{\stackrel{\to }{V}}_{1}\cdot {\stackrel{\to }{V}}_{1}=|{\stackrel{\to }{V}}_{1}{|}^{2}={V}_{1}^{2}$

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