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Gyk (vitalap | szerkesztései) Nincs szerkesztési összefoglaló |
Gyk (vitalap | szerkesztései) Nincs szerkesztési összefoglaló |
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1. sor:
[http://hu.wikipedia.org/wiki/Wikip%C3%A9dia:Hogyan_szerkessz_egy_lapot/ Segítség szerkesztéshez]<br>▼
[http://hu.wikipedia.org/wiki/Seg%C3%ADts%C3%A9g:GyIK/ GYIK]<br>
[http://hu.wikipedia.org/wiki/Wikip%C3%A9dia:Formula_le%C3%ADr%C3%B3nyelv/ TeX képletekhez]<br>
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==Vektoriális szorzat Cross product==
The [[cross product]] (also ''vector product'' or ''outer product'') differs from the dot product primarily in that the result of a cross product of two vectors is a vector.
While everything that was said above can be generalized in a straightforward manner to more than three dimensions, the cross product is only meaningful in three dimensions (although a related product exists in seven dimensions - see below).
The cross product, denoted <b>a</b>×<b>b</b>, is a vector perpendicular to both '''a''' and '''b''' and is defined as:
:<math>\mathbf{a}\times\mathbf{b}
=\left\|\mathbf{a}\right\|\left\|\mathbf{b}\right\|\sin(\theta)\,\mathbf{n}</math>
where θ is the measure of the angle between <b>a</b> and <b>b</b>, and <b>n</b> is a unit vector perpendicular to both <b>a</b> and <b>b</b>. The problem with this definition is that there are <i>two</i> unit vectors perpendicular to both <b>b</b> and <b>a</b>. Which vector is the correct one depends upon the ''orientation'' of the vector space, i.e. on the <i>handedness</i> of the coordinate system. The coordinate system '''i''', '''j''', '''k''' is called ''right handed'', if the three vectors are situated like the thumb, index finger and middle finger (pointing straight up from your palm) of your right [[hand]]. Graphically the cross product can be represented by this figure
<center>[[Image:crossproduct.png]]</center>
In such a system, '''a'''×'''b''' is defined so that '''a''', '''b''' and '''a'''×'''b''' also becomes a right handed system. If '''i''', '''j''', '''k''' is left-handed, then '''a''', '''b''' and '''a'''×'''b''' is defined to be left-handed. Because the cross product depends on the choice of coordinate systems, its result is referred to as a [[pseudovector]]. Fortunately, in nature cross products tend to come in pairs, so that the "handedness" of the coordinate system is undone by a second cross product.
The length of '''a'''×'''b''' can be interpreted as the area of the parallelogram having '''a''' and '''b''' as sides.
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