0
By "coincident", do you mean that they lie on the same plane (i.e. they are instances of the same plane)? Assuming that's what you're after: To begin with, you should have a plane equation defining each plane in the following form: ax + by + cz + d = 0 This form can be re-written in vector form as: (a,b,c) dot (x,y,z) + d = 0 Written in this form, (a,b,c) is a vector that defines the normal of the plane (a vector perpendicular to the plane), Which determines the orientation of the plane around the origin. The scalar value d defines a distance that the plane is offset from the origin, times the length of vector (a,b,c).
In case you aren't familiar with the dot product, it is a way of multiplying two vectors resulting in a scalar value that represents the angle and the magnitude of the two vectors. Specifically: v1 dot v2 = |v1| |v2| cos(theta)
where: * theta is the angle between the vectors * |v| is the length of a vector To compare the two planes, the first thing that we will want to do is "normalize" the plane equations, that is, scale them so that the length of (a,b,c) is 1.0. To do this, divide each constant in the equation by the length of the vector (a,b,c): (ax + by + cz + d) / |(a, b, c)| = 0 The normalized version of the plane equation defines the same plane as the original plane equation. The difference is that now we can readily use the dot product to determine the angle between the two plane's normals, as "v1 dot v2 = cos(theta)" when |v1| and |v2| are both equal to 1.0. The cosine of zero degrees is 1.0, so if we calculate the dot product of the normal vectors of the two planes we can determine if the normals, and thus the planes, are parallel: cos(theta) = (a1,b1,c1) dot (a2,b2,c2)
IF cos(theta) < 1.0
the planes are not parallel, and thus cannot be coincidental.
IF cos(theta) = 1.0
the planes are parallel, and may be coincidental
IF cos(theta) = -1.0
the planes are parallel, with normals facing opposite directions
the planes may be coincidental If the planes are not parallel, you don't have to test any further, they are not coincidental. If they are parallel, then you can determine if they are coincidental by comparing the normalized d from each equation to see if they are equal, flipping the sign if the normals are facing opposite directions: IF d1 = cos(theta) d2
the planes are coincident
Wiki User
∙ 16y ago
Add your answer:
Earn +20 pts
When two planes intersect do they intersect in a straight line?
Yes. If two planes are not coincident (the same plane) and are not parallel, then they intersect in one straight line.
What is coincident line?
Coincident lines are essentially two linear functions whose graphs are the same; therefore, the two lines will have the same slope and the same y-intercept. When graphed, the lines will be one on top of the other.
Number of solutions of a quadratic polynomial?
If you allow solutions that are complex numbers, then there are always two solutions, although the two solutions may be coincident so as to appear as a single solution. If limited to real solution, then two or none, although again, a coincident pair of solutions will appear as a single solution.
Do two planes intersects?
two planes intersect in one line, or the planes could be parallel. by the way there is no such thing as skew planes...
What is the word for two circles having identical circumferences A circle is both concentric and?
Concentric and coincident, perhaps.
Can two planes intersect in infinitely many points?
yes, it may be the two plane intersect at one line or the two planes are coincident.
When two planes intersect do they intersect in a straight line?
Yes. If two planes are not coincident (the same plane) and are not parallel, then they intersect in one straight line.
If two planes intersect than they intersect at exactaly one point?
Yes. If two planes are not coincident (the same plane) and are not parallel, then they intersect in one straight line.
Do Two planes always intersect in a line?
Some planes are parallel and don't intersect at all. Those that do intersect (and that are not coincident, i.e. the same plane) intersect in a line.
What are coincident roots?
Coincident is two linear measures resting exactly on top of each other. Coincident roots are roots that are equal to each other.
Two points that share the same location of a 2D sketch are said to be A. coincident B. collinear C. concentric D. coplanar?
A. Coincident
What is coincident line?
Coincident lines are essentially two linear functions whose graphs are the same; therefore, the two lines will have the same slope and the same y-intercept. When graphed, the lines will be one on top of the other.
Can perpendicular lines intersect in at least two points?
Yes, but only if they are mutually coincident.
The intersection of two planes is always a line?
Assuming that they do intersect but are not coincident, then Yes. Just to make this a little simpler, since if you're asking this, you may not understand the above answer. As long as they're not parallel, e.g., like two floors in the same building are parallel and will never meet no matter how long you extend them, then they'll meet eventually, and will form a line. Coincident just means they are in exactly the same space, and therefore are essentially identical and only one plane, and so also will not intersect.
Do two planes intersects?
two planes intersect in one line, or the planes could be parallel. by the way there is no such thing as skew planes...
Number of solutions of a quadratic polynomial?
If you allow solutions that are complex numbers, then there are always two solutions, although the two solutions may be coincident so as to appear as a single solution. If limited to real solution, then two or none, although again, a coincident pair of solutions will appear as a single solution.
What occurs when two planes intersect?
The intersection of two planes is a line.
