Mixing
Need some help with analytic geometry
$begingroup$
Check if the following point lies on the plane π : 2x − 3y + 4z − 5 = 0
- (point) A = (1, -1, 0)
Check if the following vector lies on the plane π : 2x − 3y + 4z − 5 = 0
- (vector) -AC = (1, 2, 1)
Can someone help me to solve this? With my example please, it would be great.
linear-algebra vectors analytic-geometry plane-geometry
asked Jan 14 at 20:41
Aliaksei KlimovichAliaksei Klimovich
516
$endgroup$
add a comment |
$begingroup$
Check if the following point lies on the plane π : 2x − 3y + 4z − 5 = 0
- (point) A = (1, -1, 0)
Check if the following vector lies on the plane π : 2x − 3y + 4z − 5 = 0
- (vector) -AC = (1, 2, 1)
Can someone help me to solve this? With my example please, it would be great.
linear-algebra vectors analytic-geometry plane-geometry
asked Jan 14 at 20:41
Aliaksei KlimovichAliaksei Klimovich
516
$endgroup$
$begingroup$
You have the equation. Plug in the point and see if the equation’s satisfied.
$endgroup$
– amd
Jan 14 at 21:02
add a comment |
$begingroup$
Check if the following point lies on the plane π : 2x − 3y + 4z − 5 = 0
- (point) A = (1, -1, 0)
Check if the following vector lies on the plane π : 2x − 3y + 4z − 5 = 0
- (vector) -AC = (1, 2, 1)
Can someone help me to solve this? With my example please, it would be great.
linear-algebra vectors analytic-geometry plane-geometry
asked Jan 14 at 20:41
Aliaksei KlimovichAliaksei Klimovich
516
$endgroup$
Check if the following point lies on the plane π : 2x − 3y + 4z − 5 = 0
- (point) A = (1, -1, 0)
Check if the following vector lies on the plane π : 2x − 3y + 4z − 5 = 0
- (vector) -AC = (1, 2, 1)
Can someone help me to solve this? With my example please, it would be great.
linear-algebra vectors analytic-geometry plane-geometry
linear-algebra vectors analytic-geometry plane-geometry
asked Jan 14 at 20:41
Aliaksei KlimovichAliaksei Klimovich
516
asked Jan 14 at 20:41
Aliaksei KlimovichAliaksei Klimovich
516
edited Jan 14 at 20:48
Aliaksei Klimovich
asked Jan 14 at 20:41
Aliaksei KlimovichAliaksei Klimovich
516
asked Jan 14 at 20:41
Aliaksei KlimovichAliaksei Klimovich
516
asked Jan 14 at 20:41
Aliaksei KlimovichAliaksei Klimovich
516
516
$begingroup$
You have the equation. Plug in the point and see if the equation’s satisfied.
$endgroup$
– amd
Jan 14 at 21:02
add a comment |
$begingroup$
You have the equation. Plug in the point and see if the equation’s satisfied.
$endgroup$
– amd
Jan 14 at 21:02
$begingroup$
You have the equation. Plug in the point and see if the equation’s satisfied.
$endgroup$
– amd
Jan 14 at 21:02
$begingroup$
You have the equation. Plug in the point and see if the equation’s satisfied.
$endgroup$
– amd
Jan 14 at 21:02
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
To check whether a point belongs to a plane just substitute x,y,z in you equation by the given numbers. $2*1 - 3(-1) + 4 cdot0-5=5-5=0$ <- so it does belong to your plane
If we want to check whether a vector lies on the plane it has to be perpendicular to the normal vector. To see if it is consider the following vector product: $[2,-3,4] times [1,2,1]$. If it is zero, then your vector lies on the plane.
answered Jan 14 at 20:48
The CatThe Cat
25112
$endgroup$
1
$begingroup$
Thanks a lot, it helped
$endgroup$
– Aliaksei Klimovich
Jan 14 at 20:53
add a comment |
$begingroup$
Does point A lie in the plane? How would you check that?
Now find a second point in the plane. $A+v.$
Is this point in your plane?
A different way to check to see if your vectors is parallel to your plane. Find the normal vector to your plane. $v$ perpendicular to the normal vector? (How would you check that?)
answered Jan 14 at 20:46
Doug MDoug M
45.2k31854
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
To check whether a point belongs to a plane just substitute x,y,z in you equation by the given numbers. $2*1 - 3(-1) + 4 cdot0-5=5-5=0$ <- so it does belong to your plane
If we want to check whether a vector lies on the plane it has to be perpendicular to the normal vector. To see if it is consider the following vector product: $[2,-3,4] times [1,2,1]$. If it is zero, then your vector lies on the plane.
answered Jan 14 at 20:48
The CatThe Cat
25112
$endgroup$
1
$begingroup$
Thanks a lot, it helped
$endgroup$
– Aliaksei Klimovich
Jan 14 at 20:53
add a comment |
$begingroup$
To check whether a point belongs to a plane just substitute x,y,z in you equation by the given numbers. $2*1 - 3(-1) + 4 cdot0-5=5-5=0$ <- so it does belong to your plane
If we want to check whether a vector lies on the plane it has to be perpendicular to the normal vector. To see if it is consider the following vector product: $[2,-3,4] times [1,2,1]$. If it is zero, then your vector lies on the plane.
answered Jan 14 at 20:48
The CatThe Cat
25112
$endgroup$
1
$begingroup$
Thanks a lot, it helped
$endgroup$
– Aliaksei Klimovich
Jan 14 at 20:53
add a comment |
$begingroup$
To check whether a point belongs to a plane just substitute x,y,z in you equation by the given numbers. $2*1 - 3(-1) + 4 cdot0-5=5-5=0$ <- so it does belong to your plane
If we want to check whether a vector lies on the plane it has to be perpendicular to the normal vector. To see if it is consider the following vector product: $[2,-3,4] times [1,2,1]$. If it is zero, then your vector lies on the plane.
answered Jan 14 at 20:48
The CatThe Cat
25112
$endgroup$
To check whether a point belongs to a plane just substitute x,y,z in you equation by the given numbers. $2*1 - 3(-1) + 4 cdot0-5=5-5=0$ <- so it does belong to your plane
If we want to check whether a vector lies on the plane it has to be perpendicular to the normal vector. To see if it is consider the following vector product: $[2,-3,4] times [1,2,1]$. If it is zero, then your vector lies on the plane.
answered Jan 14 at 20:48
The CatThe Cat
25112
answered Jan 14 at 20:48
The CatThe Cat
25112
answered Jan 14 at 20:48
The CatThe Cat
25112
answered Jan 14 at 20:48
The CatThe Cat
25112
25112
1
$begingroup$
Thanks a lot, it helped
$endgroup$
– Aliaksei Klimovich
Jan 14 at 20:53
add a comment |
1
$begingroup$
Thanks a lot, it helped
$endgroup$
– Aliaksei Klimovich
Jan 14 at 20:53
1
1
$begingroup$
Thanks a lot, it helped
$endgroup$
– Aliaksei Klimovich
Jan 14 at 20:53
$begingroup$
Thanks a lot, it helped
$endgroup$
– Aliaksei Klimovich
Jan 14 at 20:53
add a comment |
$begingroup$
Does point A lie in the plane? How would you check that?
Now find a second point in the plane. $A+v.$
Is this point in your plane?
A different way to check to see if your vectors is parallel to your plane. Find the normal vector to your plane. $v$ perpendicular to the normal vector? (How would you check that?)
answered Jan 14 at 20:46
Doug MDoug M
45.2k31854
$endgroup$
add a comment |
$begingroup$
Does point A lie in the plane? How would you check that?
Now find a second point in the plane. $A+v.$
Is this point in your plane?
A different way to check to see if your vectors is parallel to your plane. Find the normal vector to your plane. $v$ perpendicular to the normal vector? (How would you check that?)
answered Jan 14 at 20:46
Doug MDoug M
45.2k31854
$endgroup$
add a comment |
$begingroup$
Does point A lie in the plane? How would you check that?
Now find a second point in the plane. $A+v.$
Is this point in your plane?
A different way to check to see if your vectors is parallel to your plane. Find the normal vector to your plane. $v$ perpendicular to the normal vector? (How would you check that?)
answered Jan 14 at 20:46
Doug MDoug M
45.2k31854
$endgroup$
Does point A lie in the plane? How would you check that?
Now find a second point in the plane. $A+v.$
Is this point in your plane?
A different way to check to see if your vectors is parallel to your plane. Find the normal vector to your plane. $v$ perpendicular to the normal vector? (How would you check that?)
answered Jan 14 at 20:46
Doug MDoug M
45.2k31854
answered Jan 14 at 20:46
Doug MDoug M
45.2k31854
answered Jan 14 at 20:46
Doug MDoug M
45.2k31854
answered Jan 14 at 20:46
Doug MDoug M
45.2k31854
45.2k31854
add a comment |
add a comment |
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$begingroup$
You have the equation. Plug in the point and see if the equation’s satisfied.
$endgroup$
– amd
Jan 14 at 21:02