<![CDATA[Math Is Fun Forum / Vector Formulas]]> 2018-01-27T07:09:29Z FluxBB http://www.mathisfunforum.com/viewtopic.php?id=3289 <![CDATA[Re: Vector Formulas]]> ganesh wrote:

Where is the supposed "c" in the Left Hand Side?

]]>
http://www.mathisfunforum.com/profile.php?id=212031 2018-01-27T07:09:29Z http://www.mathisfunforum.com/viewtopic.php?pid=401881#p401881
<![CDATA[Re: Vector Formulas]]> The equation of a line in vector form

A vector equation of a straight line passing through the point A with with position vector a, and parallel to the vector b, is

A vector equation of a straight line passing through the points C and D, with position vectors c and d respectively, is

Where t is a scalar parameter.

]]>
http://www.mathisfunforum.com/profile.php?id=7997 2008-03-11T21:00:51Z http://www.mathisfunforum.com/viewtopic.php?pid=89636#p89636
<![CDATA[Re: Vector Formulas]]> The Laplacian

The Laplacian operator ∇[sup]2[/sup] may be used on either scalar or vector functions:

The Biharmonic Operator

The biharmonic operator ∇[sup]4[/sup] on Φ is given by

∇ Formulas

For scalar functions Φ and Θ and vector functions A and B, the following equalities hold:

]]>
http://www.mathisfunforum.com/profile.php?id=1171 2006-08-06T04:24:02Z http://www.mathisfunforum.com/viewtopic.php?pid=39036#p39036
<![CDATA[Re: Vector Formulas]]> The Operator Del/Nabla

The operator del(sometimes called nabla) is defined by

The gradient of Φ(x, y, z) is given by

Divergence

The divergence of A is given by

Curl

The curl of A is given by

]]>
http://www.mathisfunforum.com/profile.php?id=1171 2006-08-06T04:22:43Z http://www.mathisfunforum.com/viewtopic.php?pid=39035#p39035
<![CDATA[Re: Vector Formulas]]> Derivative of a Vector Function

The derivative of a vector function A(u) = A[sub]1[/sub](u)i + A[sub]2[/sub](u)j + A[sub]3[/sub](u)k is given by

Vector derivatives satisfy the following equations(note that Φ is a scalar function):

Integral of a Vector Function

If A(u) = dB/du, then we have the indefinite integral of A(u)

and the definite integral of A(u)

]]>
http://www.mathisfunforum.com/profile.php?id=1171 2006-08-06T04:17:40Z http://www.mathisfunforum.com/viewtopic.php?pid=39034#p39034
<![CDATA[Re: Vector Formulas]]> Scalar Product of four vectors

Vector product of four vectors

Vector product of four vectors

is given by

]]>
http://www.mathisfunforum.com/profile.php?id=682 2006-04-20T14:49:33Z http://www.mathisfunforum.com/viewtopic.php?pid=33642#p33642
<![CDATA[Re: Vector Formulas]]> Vector Triple Product

The Vector Triple Product of three vectors

is defined as

Vector triple product is not associative.

]]>
http://www.mathisfunforum.com/profile.php?id=682 2006-04-19T15:45:50Z http://www.mathisfunforum.com/viewtopic.php?pid=33611#p33611
<![CDATA[Re: Vector Formulas]]> Scalar Triple Product

If

then

is also represented as

Interchanging any two vectors in the scalar triple product changes the sign of the scalar triple product.

If any of the two vectors are equal, then

is the volume of the Parellopiped whose coterminus edges are formed by

If

are coplanar,

]]>
http://www.mathisfunforum.com/profile.php?id=682 2006-04-19T14:26:58Z http://www.mathisfunforum.com/viewtopic.php?pid=33609#p33609
<![CDATA[Re: Vector Formulas]]> Cross Product or Vector product

]]>
http://www.mathisfunforum.com/profile.php?id=682 2006-04-17T15:42:09Z http://www.mathisfunforum.com/viewtopic.php?pid=33544#p33544
<![CDATA[Re: Vector Formulas]]> Ganesh, you can use \cdot to produce:

]]>
http://www.mathisfunforum.com/profile.php?id=2143 2006-04-15T01:05:12Z http://www.mathisfunforum.com/viewtopic.php?pid=33354#p33354
<![CDATA[Re: Vector Formulas]]> Scalar Product

where
is the angle between the two vectors.
If

and

then

and

]]>
http://www.mathisfunforum.com/profile.php?id=682 2006-04-08T16:20:16Z http://www.mathisfunforum.com/viewtopic.php?pid=33117#p33117
<![CDATA[Re: Vector Formulas]]> Let
and
be any two vectors.

Properties:-

(i) Commutativity

(ii) Associativity:-

(iii) Existence of a negative vector:
For every vector

, there is a negative such that

If m and n are scalars,

(iv)

(v)

(vi)

(vii)

(viii)

]]>
http://www.mathisfunforum.com/profile.php?id=682 2006-04-08T16:00:54Z http://www.mathisfunforum.com/viewtopic.php?pid=33116#p33116
<![CDATA[Vector Formulas]]> Vector Formulas

]]>
http://www.mathisfunforum.com/profile.php?id=2 2006-03-29T22:00:45Z http://www.mathisfunforum.com/viewtopic.php?pid=32566#p32566