How would I use the dot product of $u$ $u$ if $u$ $u$ $=$ $=$ $5 i$ $5i$ $+$ $+$ $2 j$ $2j$ ?

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How would I use the dot product of $u$ $u$ if $u$ $u$ $=$ $=$ $5 i$ $5i$ $+$ $+$ $2 j$ $2j$ ?

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Answer 1 · 2016-06-06T17:00:39

The dot product (also called Euclidean inner product) of any 2 n-dimensional vectors is a scalar real or complex numbers.

So the dot product is an operator which operates on 2 vectors to produce a real or complex number.

Hence you cannot have the dot product of just 1 vector.

For example, let $v = 4 i + 3 j$ $v=4i+3j$ be another 2 dimensional vector.

Then the dot product of $u$ $u$ with $v$ $v$ is

$u \cdot v = (5 i + 2 j) \cdot (4 i + 3 j)$ $u*v=(5i+2j)*(4i+3j)$

$= (5 \times 4) + (2 \times 3)$ $=(5xx4)+(2xx3)$

$= 26$ $=26$ .

Note that we may take the dot product of a vector with itself (not sure if that is what you meant to ask), and in that case we get it equal to the norm of the vector squared, that is

$u \cdot u = {| | u | |}^{2} = {(\sqrt{5^{2} + 2^{2}})}^{2} = {(\sqrt{29})}^{2} = 29$ $u*u=||u||^2=(sqrt(5^2+2^2))^2=(sqrt29)^2=29$ .

The dot product has many uses and applications in everyday life.
For example, in mechanics we define work to be the dot product between the resultant force and the displacement. $W = F \cdot x$ $W=F*x$ .
The magnitude hereof may then be evaluated as $F x cos θ$ $Fxcostheta$ where $θ$ $theta$ is the angle between $F and x$ $F and x$ .

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How would I use the dot product of $u$ $u$ if $u$ $u$ $=$ $=$ $5 i$ $5i$ $+$ $+$ $2 j$ $2j$ ?

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How would I use the dot product of uu if uu==5i5i++2j2j?

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How would I use the dot product of $u$ $u$ if $u$ $u$ $=$ $=$ $5 i$ $5i$ $+$ $+$ $2 j$ $2j$ ?