Scalar product: Difference between revisions

Latest revision as of 16:49, 25 April 2012

scalar product

(Also called dot product, direct product, inner product.) A scalar equal to the product of the magnitudes of any two vectors and the cosine of the angle θ between their positive directions.

For two vectors A and B, the scalar product is most commonly written A · B, read "A dot B," and occasionally as (AB). If the vectors A and B have the components A_x, B_x, A_y, B_y, and A_z, B_z along rectangular Cartesian x, y, and z axes, respectively, then

If a scalar product is zero, one of the vectors is zero or else the two are perpendicular.
See vector product.

INDEX
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
0
1
2
3
4
5
6
7
8
9

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-<div class="definition"><div class="short_definition">(<br/>''Also called'' dot product, direct product, inner product.) A [[scalar]] equal to the  product of the magnitudes of any two [[vectors]] and the cosine of the angle &#x003b8; between their positive  directions.</div><br/> <div class="paragraph">For two vectors '''A''' and '''B''', the scalar product is most commonly written '''A''' &middot; '''B''', read &ldquo;'''A''' dot '''B''',&rdquo;  and occasionally as ('''AB'''). If the vectors '''A''' and '''B''' have the components ''A''<sub>x</sub>, ''B''<sub>x</sub>, ''A''<sub>y</sub>, ''B''<sub>y</sub>, and ''A''<sub>z</sub>, ''B''<sub>z</sub>  along rectangular Cartesian ''x'', ''y'', and ''z'' axes, respectively, then  <div class="display-formula"><blockquote>[[File:ams2001glos-Se7.gif|link=|center|ams2001glos-Se7]]</blockquote></div> If a scalar product is zero, one of the vectors is zero or else the two are perpendicular. <br/>''See'' [[vector  product]].</div><br/> </div>
+<div class="definition"><div class="short_definition">(''Also called'' dot product, direct product, inner product.) A [[scalar]] equal to the  product of the magnitudes of any two [[vectors]] and the cosine of the angle &#x003b8; between their positive  directions.</div><br/> <div class="paragraph">For two vectors '''A''' and '''B''', the scalar product is most commonly written '''A''' &middot; '''B''', read "'''A''' dot '''B''',"  and occasionally as ('''AB'''). If the vectors '''A''' and '''B''' have the components ''A''<sub>x</sub>, ''B''<sub>x</sub>, ''A''<sub>y</sub>, ''B''<sub>y</sub>, and ''A''<sub>z</sub>, ''B''<sub>z</sub>  along rectangular Cartesian ''x'', ''y'', and ''z'' axes, respectively, then  <div class="display-formula"><blockquote>[[File:ams2001glos-Se7.gif|link=|center|ams2001glos-Se7]]</blockquote></div> If a scalar product is zero, one of the vectors is zero or else the two are perpendicular. <br/>''See'' [[vector product|vector  product]].</div><br/> </div>
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