Vectors: equation [closed]
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Let $vec{a} in mathbb{R}^3, vec{a}neq 0 $. How can I solve this equation: $ vec{x}times (vec{x} times vec{a})=vec{a} times (vec{a} times vec{x})$?
linear-algebra vectors
asked Dec 2 at 14:58
nene123
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closed as off-topic by José Carlos Santos, user302797, caverac, amWhy, Ali Caglayan Dec 2 at 20:18
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, user302797, caverac, amWhy, Ali Caglayan
If this question can be reworded to fit the rules in the help center, please edit the question.
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Let $vec{a} in mathbb{R}^3, vec{a}neq 0 $. How can I solve this equation: $ vec{x}times (vec{x} times vec{a})=vec{a} times (vec{a} times vec{x})$?
linear-algebra vectors
asked Dec 2 at 14:58
nene123
52
New contributor
nene123 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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closed as off-topic by José Carlos Santos, user302797, caverac, amWhy, Ali Caglayan Dec 2 at 20:18
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, user302797, caverac, amWhy, Ali Caglayan
If this question can be reworded to fit the rules in the help center, please edit the question.
3
Do you mean $vec ainBbb R^3$?
– Arthur
Dec 2 at 15:01
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up vote
-1
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up vote
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down vote
favorite
Let $vec{a} in mathbb{R}^3, vec{a}neq 0 $. How can I solve this equation: $ vec{x}times (vec{x} times vec{a})=vec{a} times (vec{a} times vec{x})$?
linear-algebra vectors
asked Dec 2 at 14:58
nene123
52
New contributor
nene123 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Let $vec{a} in mathbb{R}^3, vec{a}neq 0 $. How can I solve this equation: $ vec{x}times (vec{x} times vec{a})=vec{a} times (vec{a} times vec{x})$?
linear-algebra vectors
linear-algebra vectors
asked Dec 2 at 14:58
nene123
52
New contributor
nene123 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Dec 2 at 14:58
nene123
52
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nene123 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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edited Dec 2 at 15:06
asked Dec 2 at 14:58
nene123
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nene123 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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asked Dec 2 at 14:58
nene123
52
asked Dec 2 at 14:58
nene123
52
52
New contributor
nene123 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
nene123 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
nene123 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
closed as off-topic by José Carlos Santos, user302797, caverac, amWhy, Ali Caglayan Dec 2 at 20:18
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, user302797, caverac, amWhy, Ali Caglayan
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by José Carlos Santos, user302797, caverac, amWhy, Ali Caglayan Dec 2 at 20:18
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, user302797, caverac, amWhy, Ali Caglayan
If this question can be reworded to fit the rules in the help center, please edit the question.
3
Do you mean $vec ainBbb R^3$?
– Arthur
Dec 2 at 15:01
add a comment |
3
Do you mean $vec ainBbb R^3$?
– Arthur
Dec 2 at 15:01
3
3
Do you mean $vec ainBbb R^3$?
– Arthur
Dec 2 at 15:01
Do you mean $vec ainBbb R^3$?
– Arthur
Dec 2 at 15:01
add a comment |
1 Answer
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$vec{x}times (vec{x} times vec{a})=vec{a} times (vec{a} times vec{x})=-vec{a} times (vec{x}times vec{a})implies (vec x+vec a)times(vec xtimes vec a)=vec0$
For non-zero $vec a, vec x$, we have either $vec x+vec a=vec 0$ or $vec xtimes vec a=vec0$ or $(vec x+vec a) parallel (vec xtimes vec a)$. The last case is not possible as $vec xtimes vec a$ is perpendicular to the plane containing $vec x, vec a$ and $vec x+vec a$.
$vec xtimesvec a=vec0implies vec x=kvec a, kinmathbb R$
answered Dec 2 at 15:15
Shubham Johri
1,28039
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
accepted
$vec{x}times (vec{x} times vec{a})=vec{a} times (vec{a} times vec{x})=-vec{a} times (vec{x}times vec{a})implies (vec x+vec a)times(vec xtimes vec a)=vec0$
For non-zero $vec a, vec x$, we have either $vec x+vec a=vec 0$ or $vec xtimes vec a=vec0$ or $(vec x+vec a) parallel (vec xtimes vec a)$. The last case is not possible as $vec xtimes vec a$ is perpendicular to the plane containing $vec x, vec a$ and $vec x+vec a$.
$vec xtimesvec a=vec0implies vec x=kvec a, kinmathbb R$
answered Dec 2 at 15:15
Shubham Johri
1,28039
add a comment |
up vote
0
down vote
accepted
$vec{x}times (vec{x} times vec{a})=vec{a} times (vec{a} times vec{x})=-vec{a} times (vec{x}times vec{a})implies (vec x+vec a)times(vec xtimes vec a)=vec0$
For non-zero $vec a, vec x$, we have either $vec x+vec a=vec 0$ or $vec xtimes vec a=vec0$ or $(vec x+vec a) parallel (vec xtimes vec a)$. The last case is not possible as $vec xtimes vec a$ is perpendicular to the plane containing $vec x, vec a$ and $vec x+vec a$.
$vec xtimesvec a=vec0implies vec x=kvec a, kinmathbb R$
answered Dec 2 at 15:15
Shubham Johri
1,28039
add a comment |
up vote
0
down vote
accepted
up vote
0
down vote
accepted
$vec{x}times (vec{x} times vec{a})=vec{a} times (vec{a} times vec{x})=-vec{a} times (vec{x}times vec{a})implies (vec x+vec a)times(vec xtimes vec a)=vec0$
For non-zero $vec a, vec x$, we have either $vec x+vec a=vec 0$ or $vec xtimes vec a=vec0$ or $(vec x+vec a) parallel (vec xtimes vec a)$. The last case is not possible as $vec xtimes vec a$ is perpendicular to the plane containing $vec x, vec a$ and $vec x+vec a$.
$vec xtimesvec a=vec0implies vec x=kvec a, kinmathbb R$
answered Dec 2 at 15:15
Shubham Johri
1,28039
$vec{x}times (vec{x} times vec{a})=vec{a} times (vec{a} times vec{x})=-vec{a} times (vec{x}times vec{a})implies (vec x+vec a)times(vec xtimes vec a)=vec0$
For non-zero $vec a, vec x$, we have either $vec x+vec a=vec 0$ or $vec xtimes vec a=vec0$ or $(vec x+vec a) parallel (vec xtimes vec a)$. The last case is not possible as $vec xtimes vec a$ is perpendicular to the plane containing $vec x, vec a$ and $vec x+vec a$.
$vec xtimesvec a=vec0implies vec x=kvec a, kinmathbb R$
answered Dec 2 at 15:15
Shubham Johri
1,28039
edited Dec 2 at 15:43
answered Dec 2 at 15:15
Shubham Johri
1,28039
answered Dec 2 at 15:15
Shubham Johri
1,28039
answered Dec 2 at 15:15
Shubham Johri
1,28039
1,28039
add a comment |
add a comment |
3
Do you mean $vec ainBbb R^3$?
– Arthur
Dec 2 at 15:01