Cross product related question [closed]

-1

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 $mathbb{R}^{3}$.

edited Dec 27 '18 at 23:06

Eric Wofsey

193k14220352

asked Dec 27 '18 at 18:26

Atanu Mondal

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

add a comment |

-1

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 $mathbb{R}^{3}$.

edited Dec 27 '18 at 23:06

Eric Wofsey

193k14220352

asked Dec 27 '18 at 18:26

Atanu Mondal

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

add a comment |

-1

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 $mathbb{R}^{3}$.

edited Dec 27 '18 at 23:06

Eric Wofsey

193k14220352

asked Dec 27 '18 at 18:26

Atanu Mondal

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

edited Dec 27 '18 at 23:06

Eric Wofsey

193k14220352

asked Dec 27 '18 at 18:26

Atanu Mondal

edited Dec 27 '18 at 23:06

Eric Wofsey

193k14220352

asked Dec 27 '18 at 18:26

Atanu Mondal

edited Dec 27 '18 at 23:06

Eric Wofsey

193k14220352

edited Dec 27 '18 at 23:06

Eric Wofsey

193k14220352

edited Dec 27 '18 at 23:06

Eric Wofsey

193k14220352

asked Dec 27 '18 at 18:26

Atanu Mondal

asked Dec 27 '18 at 18:26

Atanu Mondal

asked Dec 27 '18 at 18:26

Atanu Mondal

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

add a comment |

1

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

Can you put any context and/or what have you tried?

– Tito Eliatron
Dec 27 '18 at 18:27

add a comment |

1 Answer
1

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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.

answered Dec 27 '18 at 18:56

Alex R.

25.2k12452

add a comment |

1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

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.

answered Dec 27 '18 at 18:56

Alex R.

25.2k12452

add a comment |

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.

answered Dec 27 '18 at 18:56

Alex R.

25.2k12452

add a comment |

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.

answered Dec 27 '18 at 18:56

Alex R.

25.2k12452

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.

answered Dec 27 '18 at 18:56

Alex R.

25.2k12452

answered Dec 27 '18 at 18:56

Alex R.

25.2k12452

answered Dec 27 '18 at 18:56

Alex R.

25.2k12452

answered Dec 27 '18 at 18:56

Alex R.

25.2k12452

add a comment |

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