Vector/linear algebra Plane Question english explanation
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I am not a native English speaker but I study a vector/linear algebra course in English. I am having trouble understanding what this particular question actually means. I have seen the solution and I know how to get there but I am not sure what I am actually doing or what the question wants me to do. I managed to solve this by following calculations of a similar example question.
"In Exercises 73-76, find a point-normal form of the equation of the plane passing through P and having n as a normal"
P(2,3,-4) n=(1,-1,2)
linear-algebra
asked Nov 27 at 12:33
J. Doe
484
add a comment |
up vote
0
down vote
favorite
I am not a native English speaker but I study a vector/linear algebra course in English. I am having trouble understanding what this particular question actually means. I have seen the solution and I know how to get there but I am not sure what I am actually doing or what the question wants me to do. I managed to solve this by following calculations of a similar example question.
"In Exercises 73-76, find a point-normal form of the equation of the plane passing through P and having n as a normal"
P(2,3,-4) n=(1,-1,2)
linear-algebra
asked Nov 27 at 12:33
J. Doe
484
Do you know what "point-normal" means?
– 5xum
Nov 27 at 12:35
What do you mean by a point-normal form?
– Bernard
Nov 27 at 12:36
I know that normal is a orthogonal vector to the plane, I do not know what point normal mean
– J. Doe
Nov 27 at 12:38
A simple internet search for “point-normal form” turns up this, this, this and many other sources.
– amd
Nov 28 at 0:03
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I am not a native English speaker but I study a vector/linear algebra course in English. I am having trouble understanding what this particular question actually means. I have seen the solution and I know how to get there but I am not sure what I am actually doing or what the question wants me to do. I managed to solve this by following calculations of a similar example question.
"In Exercises 73-76, find a point-normal form of the equation of the plane passing through P and having n as a normal"
P(2,3,-4) n=(1,-1,2)
linear-algebra
asked Nov 27 at 12:33
J. Doe
484
I am not a native English speaker but I study a vector/linear algebra course in English. I am having trouble understanding what this particular question actually means. I have seen the solution and I know how to get there but I am not sure what I am actually doing or what the question wants me to do. I managed to solve this by following calculations of a similar example question.
"In Exercises 73-76, find a point-normal form of the equation of the plane passing through P and having n as a normal"
P(2,3,-4) n=(1,-1,2)
linear-algebra
linear-algebra
asked Nov 27 at 12:33
J. Doe
484
asked Nov 27 at 12:33
J. Doe
484
asked Nov 27 at 12:33
J. Doe
484
asked Nov 27 at 12:33
J. Doe
484
asked Nov 27 at 12:33
J. Doe
484
484
Do you know what "point-normal" means?
– 5xum
Nov 27 at 12:35
What do you mean by a point-normal form?
– Bernard
Nov 27 at 12:36
I know that normal is a orthogonal vector to the plane, I do not know what point normal mean
– J. Doe
Nov 27 at 12:38
A simple internet search for “point-normal form” turns up this, this, this and many other sources.
– amd
Nov 28 at 0:03
add a comment |
Do you know what "point-normal" means?
– 5xum
Nov 27 at 12:35
What do you mean by a point-normal form?
– Bernard
Nov 27 at 12:36
I know that normal is a orthogonal vector to the plane, I do not know what point normal mean
– J. Doe
Nov 27 at 12:38
A simple internet search for “point-normal form” turns up this, this, this and many other sources.
– amd
Nov 28 at 0:03
Do you know what "point-normal" means?
– 5xum
Nov 27 at 12:35
Do you know what "point-normal" means?
– 5xum
Nov 27 at 12:35
What do you mean by a point-normal form?
– Bernard
Nov 27 at 12:36
What do you mean by a point-normal form?
– Bernard
Nov 27 at 12:36
I know that normal is a orthogonal vector to the plane, I do not know what point normal mean
– J. Doe
Nov 27 at 12:38
I know that normal is a orthogonal vector to the plane, I do not know what point normal mean
– J. Doe
Nov 27 at 12:38
A simple internet search for “point-normal form” turns up this, this, this and many other sources.
– amd
Nov 28 at 0:03
A simple internet search for “point-normal form” turns up this, this, this and many other sources.
– amd
Nov 28 at 0:03
add a comment |
3 Answers
3
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1
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accepted
If $(x_0,y_0,z_0)$ is a point in the plane and $vec{n}=langle n_x,n_y,n_zrangle$ is normal to the plane, then the point-normal equation for the plane is
$$
n_x(x-x_0)+n_y(y-y_0)+n_z(z-z_0)=0.
$$
answered Nov 27 at 12:52
Michael Burr
26.4k23262
add a comment |
up vote
0
down vote
Pick a point $(x,y,z)$ in the plane, then the vector $(x-2,y-3,z+4)$ is a vector in the plane. Therefore the dot product of the vector and the normal vector is $0$ so we get $(x-2)-(y-3)+2(z+4)=0$(This is the point normal form) which is the same as $x-2-y+3+2z+8=0$ which is the same as $x-y+2z=-9$.
answered Nov 27 at 12:43
mathnoob
1,646322
add a comment |
up vote
0
down vote
Consider the equation of the plane: ax+by+cz=c. This is of the form f(x,y,z)=c, which is level to the the function f(x,y,z). Since the gradient $nabla$f(x,y,z) is always perpendicular to the level of a function. So that means that the normal is $<a,b,c>$. Do you know how to find the equation of the plane?
answered Nov 27 at 13:37
maths researcher
458
add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
If $(x_0,y_0,z_0)$ is a point in the plane and $vec{n}=langle n_x,n_y,n_zrangle$ is normal to the plane, then the point-normal equation for the plane is
$$
n_x(x-x_0)+n_y(y-y_0)+n_z(z-z_0)=0.
$$
answered Nov 27 at 12:52
Michael Burr
26.4k23262
add a comment |
up vote
1
down vote
accepted
If $(x_0,y_0,z_0)$ is a point in the plane and $vec{n}=langle n_x,n_y,n_zrangle$ is normal to the plane, then the point-normal equation for the plane is
$$
n_x(x-x_0)+n_y(y-y_0)+n_z(z-z_0)=0.
$$
answered Nov 27 at 12:52
Michael Burr
26.4k23262
add a comment |
up vote
1
down vote
accepted
up vote
1
down vote
accepted
If $(x_0,y_0,z_0)$ is a point in the plane and $vec{n}=langle n_x,n_y,n_zrangle$ is normal to the plane, then the point-normal equation for the plane is
$$
n_x(x-x_0)+n_y(y-y_0)+n_z(z-z_0)=0.
$$
answered Nov 27 at 12:52
Michael Burr
26.4k23262
If $(x_0,y_0,z_0)$ is a point in the plane and $vec{n}=langle n_x,n_y,n_zrangle$ is normal to the plane, then the point-normal equation for the plane is
$$
n_x(x-x_0)+n_y(y-y_0)+n_z(z-z_0)=0.
$$
answered Nov 27 at 12:52
Michael Burr
26.4k23262
answered Nov 27 at 12:52
Michael Burr
26.4k23262
answered Nov 27 at 12:52
Michael Burr
26.4k23262
answered Nov 27 at 12:52
Michael Burr
26.4k23262
26.4k23262
add a comment |
add a comment |
up vote
0
down vote
Pick a point $(x,y,z)$ in the plane, then the vector $(x-2,y-3,z+4)$ is a vector in the plane. Therefore the dot product of the vector and the normal vector is $0$ so we get $(x-2)-(y-3)+2(z+4)=0$(This is the point normal form) which is the same as $x-2-y+3+2z+8=0$ which is the same as $x-y+2z=-9$.
answered Nov 27 at 12:43
mathnoob
1,646322
add a comment |
up vote
0
down vote
Pick a point $(x,y,z)$ in the plane, then the vector $(x-2,y-3,z+4)$ is a vector in the plane. Therefore the dot product of the vector and the normal vector is $0$ so we get $(x-2)-(y-3)+2(z+4)=0$(This is the point normal form) which is the same as $x-2-y+3+2z+8=0$ which is the same as $x-y+2z=-9$.
answered Nov 27 at 12:43
mathnoob
1,646322
add a comment |
up vote
0
down vote
up vote
0
down vote
Pick a point $(x,y,z)$ in the plane, then the vector $(x-2,y-3,z+4)$ is a vector in the plane. Therefore the dot product of the vector and the normal vector is $0$ so we get $(x-2)-(y-3)+2(z+4)=0$(This is the point normal form) which is the same as $x-2-y+3+2z+8=0$ which is the same as $x-y+2z=-9$.
answered Nov 27 at 12:43
mathnoob
1,646322
Pick a point $(x,y,z)$ in the plane, then the vector $(x-2,y-3,z+4)$ is a vector in the plane. Therefore the dot product of the vector and the normal vector is $0$ so we get $(x-2)-(y-3)+2(z+4)=0$(This is the point normal form) which is the same as $x-2-y+3+2z+8=0$ which is the same as $x-y+2z=-9$.
answered Nov 27 at 12:43
mathnoob
1,646322
answered Nov 27 at 12:43
mathnoob
1,646322
answered Nov 27 at 12:43
mathnoob
1,646322
answered Nov 27 at 12:43
mathnoob
1,646322
1,646322
add a comment |
add a comment |
up vote
0
down vote
Consider the equation of the plane: ax+by+cz=c. This is of the form f(x,y,z)=c, which is level to the the function f(x,y,z). Since the gradient $nabla$f(x,y,z) is always perpendicular to the level of a function. So that means that the normal is $<a,b,c>$. Do you know how to find the equation of the plane?
answered Nov 27 at 13:37
maths researcher
458
add a comment |
up vote
0
down vote
Consider the equation of the plane: ax+by+cz=c. This is of the form f(x,y,z)=c, which is level to the the function f(x,y,z). Since the gradient $nabla$f(x,y,z) is always perpendicular to the level of a function. So that means that the normal is $<a,b,c>$. Do you know how to find the equation of the plane?
answered Nov 27 at 13:37
maths researcher
458
add a comment |
up vote
0
down vote
up vote
0
down vote
Consider the equation of the plane: ax+by+cz=c. This is of the form f(x,y,z)=c, which is level to the the function f(x,y,z). Since the gradient $nabla$f(x,y,z) is always perpendicular to the level of a function. So that means that the normal is $<a,b,c>$. Do you know how to find the equation of the plane?
answered Nov 27 at 13:37
maths researcher
458
Consider the equation of the plane: ax+by+cz=c. This is of the form f(x,y,z)=c, which is level to the the function f(x,y,z). Since the gradient $nabla$f(x,y,z) is always perpendicular to the level of a function. So that means that the normal is $<a,b,c>$. Do you know how to find the equation of the plane?
answered Nov 27 at 13:37
maths researcher
458
answered Nov 27 at 13:37
maths researcher
458
answered Nov 27 at 13:37
maths researcher
458
answered Nov 27 at 13:37
maths researcher
458
458
add a comment |
add a comment |
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Do you know what "point-normal" means?
– 5xum
Nov 27 at 12:35
What do you mean by a point-normal form?
– Bernard
Nov 27 at 12:36
I know that normal is a orthogonal vector to the plane, I do not know what point normal mean
– J. Doe
Nov 27 at 12:38
A simple internet search for “point-normal form” turns up this, this, this and many other sources.
– amd
Nov 28 at 0:03