Cross product related question [closed]












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$begingroup$


Prove that $langle atimes b,ctimes drangle + langle btimes c,atimes drangle +langle ctimes a, btimes drangle = 0$
where $a, b, c, d$ belong to $mathbb{R}^{3}$.






linear-algebra







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closed as off-topic by Antonios-Alexandros Robotis, Davide Giraudo, Shailesh, mrtaurho, Eevee Trainer Dec 28 '18 at 3:01


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Antonios-Alexandros Robotis, Davide Giraudo, Shailesh, mrtaurho, Eevee Trainer

If this question can be reworded to fit the rules in the help center, please edit the question.












  • 1




    $begingroup$
    Can you put any context and/or what have you tried?
    $endgroup$
    – Tito Eliatron
    Dec 27 '18 at 18:27
















-1












$begingroup$


Prove that $langle atimes b,ctimes drangle + langle btimes c,atimes drangle +langle ctimes a, btimes drangle = 0$
where $a, b, c, d$ belong to $mathbb{R}^{3}$.






linear-algebra







share|cite|improve this question











$endgroup$



closed as off-topic by Antonios-Alexandros Robotis, Davide Giraudo, Shailesh, mrtaurho, Eevee Trainer Dec 28 '18 at 3:01


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Antonios-Alexandros Robotis, Davide Giraudo, Shailesh, mrtaurho, Eevee Trainer

If this question can be reworded to fit the rules in the help center, please edit the question.












  • 1




    $begingroup$
    Can you put any context and/or what have you tried?
    $endgroup$
    – Tito Eliatron
    Dec 27 '18 at 18:27














-1












-1








-1





$begingroup$


Prove that $langle atimes b,ctimes drangle + langle btimes c,atimes drangle +langle ctimes a, btimes drangle = 0$
where $a, b, c, d$ belong to $mathbb{R}^{3}$.






linear-algebra







share|cite|improve this question











$endgroup$




Prove that $langle atimes b,ctimes drangle + langle btimes c,atimes drangle +langle ctimes a, btimes drangle = 0$
where $a, b, c, d$ belong to $mathbb{R}^{3}$.






linear-algebra




linear-algebra






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 27 '18 at 23:06









Eric Wofsey

193k14220352




193k14220352










asked Dec 27 '18 at 18:26









Atanu MondalAtanu Mondal

1




1




closed as off-topic by Antonios-Alexandros Robotis, Davide Giraudo, Shailesh, mrtaurho, Eevee Trainer Dec 28 '18 at 3:01


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Antonios-Alexandros Robotis, Davide Giraudo, Shailesh, mrtaurho, Eevee Trainer

If this question can be reworded to fit the rules in the help center, please edit the question.







closed as off-topic by Antonios-Alexandros Robotis, Davide Giraudo, Shailesh, mrtaurho, Eevee Trainer Dec 28 '18 at 3:01


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Antonios-Alexandros Robotis, Davide Giraudo, Shailesh, mrtaurho, Eevee Trainer

If this question can be reworded to fit the rules in the help center, please edit the question.








  • 1




    $begingroup$
    Can you put any context and/or what have you tried?
    $endgroup$
    – Tito Eliatron
    Dec 27 '18 at 18:27














  • 1




    $begingroup$
    Can you put any context and/or what have you tried?
    $endgroup$
    – Tito Eliatron
    Dec 27 '18 at 18:27








1




1




$begingroup$
Can you put any context and/or what have you tried?
$endgroup$
– Tito Eliatron
Dec 27 '18 at 18:27




$begingroup$
Can you put any context and/or what have you tried?
$endgroup$
– Tito Eliatron
Dec 27 '18 at 18:27










1 Answer
1






active

oldest

votes


















1












$begingroup$

This is effectively a specialization of the 3-dimensional Binet-Cauchy Identity or Lagrange's Identity. First show the following (you can expand both sides to verify):



$langle atimes b,ctimes drangle = (atimes b)cdot (ctimes d)=(acdot c)(bcdot d)-(acdot d)(bcdot c).$



$langle btimes c,atimes drangle = (bcdot a)(ccdot d)-(bcdot d)(acdot c).$



$langle ctimes a,btimes drangle = (ccdot b)(acdot d)-(ccdot d)(acdot b).$



Now add them up.






share|cite|improve this answer









$endgroup$




















    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    1












    $begingroup$

    This is effectively a specialization of the 3-dimensional Binet-Cauchy Identity or Lagrange's Identity. First show the following (you can expand both sides to verify):



    $langle atimes b,ctimes drangle = (atimes b)cdot (ctimes d)=(acdot c)(bcdot d)-(acdot d)(bcdot c).$



    $langle btimes c,atimes drangle = (bcdot a)(ccdot d)-(bcdot d)(acdot c).$



    $langle ctimes a,btimes drangle = (ccdot b)(acdot d)-(ccdot d)(acdot b).$



    Now add them up.






    share|cite|improve this answer









    $endgroup$


















      1












      $begingroup$

      This is effectively a specialization of the 3-dimensional Binet-Cauchy Identity or Lagrange's Identity. First show the following (you can expand both sides to verify):



      $langle atimes b,ctimes drangle = (atimes b)cdot (ctimes d)=(acdot c)(bcdot d)-(acdot d)(bcdot c).$



      $langle btimes c,atimes drangle = (bcdot a)(ccdot d)-(bcdot d)(acdot c).$



      $langle ctimes a,btimes drangle = (ccdot b)(acdot d)-(ccdot d)(acdot b).$



      Now add them up.






      share|cite|improve this answer









      $endgroup$
















        1












        1








        1





        $begingroup$

        This is effectively a specialization of the 3-dimensional Binet-Cauchy Identity or Lagrange's Identity. First show the following (you can expand both sides to verify):



        $langle atimes b,ctimes drangle = (atimes b)cdot (ctimes d)=(acdot c)(bcdot d)-(acdot d)(bcdot c).$



        $langle btimes c,atimes drangle = (bcdot a)(ccdot d)-(bcdot d)(acdot c).$



        $langle ctimes a,btimes drangle = (ccdot b)(acdot d)-(ccdot d)(acdot b).$



        Now add them up.






        share|cite|improve this answer









        $endgroup$



        This is effectively a specialization of the 3-dimensional Binet-Cauchy Identity or Lagrange's Identity. First show the following (you can expand both sides to verify):



        $langle atimes b,ctimes drangle = (atimes b)cdot (ctimes d)=(acdot c)(bcdot d)-(acdot d)(bcdot c).$



        $langle btimes c,atimes drangle = (bcdot a)(ccdot d)-(bcdot d)(acdot c).$



        $langle ctimes a,btimes drangle = (ccdot b)(acdot d)-(ccdot d)(acdot b).$



        Now add them up.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Dec 27 '18 at 18:56









        Alex R.Alex R.

        25.2k12452




        25.2k12452















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