Jump to navigation Jump to search

General

Display information for equation id:math.244518.48 on revision:244518

* Page found: Vector calculus identities (eq math.244518.48)

(force rerendering)

Cannot find the equation data in the database. Fetching from revision text.

Occurrences on the following pages:

Hash: 9f29ee0b0cf735cfd113fd5b39d89aca

TeX (original user input):

 \left(\mathbf{A}\times\mathbf{B}\right)\times\mathbf{C}=\left(\mathbf{A}\cdot\mathbf{C}\right)\mathbf{B}-\left(\mathbf{B}\cdot\mathbf{C}\right)\mathbf{A}

TeX (checked):

\left(\mathbf {A} \times \mathbf {B} \right)\times \mathbf {C} =\left(\mathbf {A} \cdot \mathbf {C} \right)\mathbf {B} -\left(\mathbf {B} \cdot \mathbf {C} \right)\mathbf {A}

LaTeXML (experimental; uses MathML) rendering

MathML (4.953 KB / 873 B) :

( 𝐀 × 𝐁 ) × 𝐂 = ( 𝐀 𝐂 ) 𝐁 - ( 𝐁 𝐂 ) 𝐀 𝐀 𝐁 𝐂 𝐀 𝐂 𝐁 𝐁 𝐂 𝐀 {\displaystyle{\displaystyle\left(\mathbf{A}\times\mathbf{B}\right)\times% \mathbf{C}=\left(\mathbf{A}\cdot\mathbf{C}\right)\mathbf{B}-\left(\mathbf{B}% \cdot\mathbf{C}\right)\mathbf{A}}}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle\left(\mathbf{A}\times\mathbf{B}\right)\times%&#10;\mathbf{C}=\left(\mathbf{A}\cdot\mathbf{C}\right)\mathbf{B}-\left(\mathbf{B}%&#10;\cdot\mathbf{C}\right)\mathbf{A}}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.22" xref="p1.1.m1.1.22.cmml">
      <mrow id="p1.1.m1.1.22.1" xref="p1.1.m1.1.22.1.cmml">
        <mrow id="p1.1.m1.1.22.1.1" xref="p1.1.m1.1.22.1.1.2.cmml">
          <mo id="p1.1.m1.1.1" xref="p1.1.m1.1.22.1.1.2.cmml">(</mo>
          <mrow id="p1.1.m1.1.22.1.1.2" xref="p1.1.m1.1.22.1.1.2.cmml">
            <mi id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">𝐀</mi>
            <mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">×</mo>
            <mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">𝐁</mi>
          </mrow>
          <mo id="p1.1.m1.1.5" xref="p1.1.m1.1.22.1.1.2.cmml">)</mo>
        </mrow>
        <mo id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">×</mo>
        <mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">𝐂</mi>
      </mrow>
      <mo id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">=</mo>
      <mrow id="p1.1.m1.1.22.2" xref="p1.1.m1.1.22.2.cmml">
        <mrow id="p1.1.m1.1.22.2.1" xref="p1.1.m1.1.22.2.1.cmml">
          <mrow id="p1.1.m1.1.22.2.1.2" xref="p1.1.m1.1.22.2.1.2.2.cmml">
            <mo id="p1.1.m1.1.9" xref="p1.1.m1.1.22.2.1.2.2.cmml">(</mo>
            <mrow id="p1.1.m1.1.22.2.1.2.2" xref="p1.1.m1.1.22.2.1.2.2.cmml">
              <mi id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">𝐀</mi>
              <mo id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml"></mo>
              <mi id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">𝐂</mi>
            </mrow>
            <mo id="p1.1.m1.1.13" xref="p1.1.m1.1.22.2.1.2.2.cmml">)</mo>
          </mrow>
          <mo id="p1.1.m1.1.22.2.1.1" xref="p1.1.m1.1.22.2.1.1.cmml"></mo>
          <mi id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">𝐁</mi>
        </mrow>
        <mo id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">-</mo>
        <mrow id="p1.1.m1.1.22.2.2" xref="p1.1.m1.1.22.2.2.cmml">
          <mrow id="p1.1.m1.1.22.2.2.2" xref="p1.1.m1.1.22.2.2.2.2.cmml">
            <mo id="p1.1.m1.1.16" xref="p1.1.m1.1.22.2.2.2.2.cmml">(</mo>
            <mrow id="p1.1.m1.1.22.2.2.2.2" xref="p1.1.m1.1.22.2.2.2.2.cmml">
              <mi id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">𝐁</mi>
              <mo id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml"></mo>
              <mi id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">𝐂</mi>
            </mrow>
            <mo id="p1.1.m1.1.20" xref="p1.1.m1.1.22.2.2.2.2.cmml">)</mo>
          </mrow>
          <mo id="p1.1.m1.1.22.2.2.1" xref="p1.1.m1.1.22.2.2.1.cmml"></mo>
          <mi id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">𝐀</mi>
        </mrow>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.22.cmml" xref="p1.1.m1.1.22">
        <eq id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8"/>
        <apply id="p1.1.m1.1.22.1.cmml" xref="p1.1.m1.1.22.1">
          <times id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6"/>
          <apply id="p1.1.m1.1.22.1.1.2.cmml" xref="p1.1.m1.1.22.1.1">
            <times id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
            <ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">𝐀</ci>
            <ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">𝐁</ci>
          </apply>
          <ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">𝐂</ci>
        </apply>
        <apply id="p1.1.m1.1.22.2.cmml" xref="p1.1.m1.1.22.2">
          <minus id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15"/>
          <apply id="p1.1.m1.1.22.2.1.cmml" xref="p1.1.m1.1.22.2.1">
            <times id="p1.1.m1.1.22.2.1.1.cmml" xref="p1.1.m1.1.22.2.1.1"/>
            <apply id="p1.1.m1.1.22.2.1.2.2.cmml" xref="p1.1.m1.1.22.2.1.2">
              <ci id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11"></ci>
              <ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">𝐀</ci>
              <ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">𝐂</ci>
            </apply>
            <ci id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">𝐁</ci>
          </apply>
          <apply id="p1.1.m1.1.22.2.2.cmml" xref="p1.1.m1.1.22.2.2">
            <times id="p1.1.m1.1.22.2.2.1.cmml" xref="p1.1.m1.1.22.2.2.1"/>
            <apply id="p1.1.m1.1.22.2.2.2.2.cmml" xref="p1.1.m1.1.22.2.2.2">
              <ci id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18"></ci>
              <ci id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">𝐁</ci>
              <ci id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19">𝐂</ci>
            </apply>
            <ci id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21">𝐀</ci>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle\left(\mathbf{A}\times\mathbf{B}\right)\times%
\mathbf{C}=\left(\mathbf{A}\cdot\mathbf{C}\right)\mathbf{B}-\left(\mathbf{B}%
\cdot\mathbf{C}\right)\mathbf{A}}}</annotation>
  </semantics>
</math>

SVG (6.75 KB / 2.072 KB) :

left-parenthesis bold upper A times bold upper B right-parenthesis times bold upper C equals left-parenthesis bold upper A dot bold upper C right-parenthesis times bold upper B minus left-parenthesis bold upper B dot bold upper C right-parenthesis times bold upper A

MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools) rendering

MathML (0 B / 8 B) :

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


PNG (0 B / 8 B) :


Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Cannot translate operation \times - Reason: An unknown or missing element occurred

Translation to Mathematica

In Mathematica:

Cannot translate operation \times - Reason: An unknown or missing element occurred

Similar pages

Calculated based on the variables occurring on the entire Vector calculus identities page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results