- #1
cscott
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What's the easiest way to make up two equations of a plane that intersect at a line?
TD said:What are you looking for, the equation of the line of intersection? Because "two equations of a plane" doesn't really make sense to me...
vaishakh said:Lines which are not parallel intersect with each other. so don't make them parallel. lines are parallel if their slopes are same. so think what have you to change or not to? A, B, C or D
I'm still not 100% sure what you mean but I *think* you mean that you're looking for the equations of two planes which, together as a system, form the equation of their intersection line (assuming the planes weren't parallel). Is this correct?cscott said:I need two equations (Ax + By + Cz + D = 0) that describe two planes who's intersection point is a line.
TD said:I'm still not 100% sure what you mean but I *think* you mean that you're looking for the equations of two planes which, together as a system, form the equation of their intersection line (assuming the planes weren't parallel). Is this correct?
fomenkoa said:Scott: This is pretty easy!
The only thing u do is make sure both bormal vectors are not scalar multiples of each other... in other words
if P1 = Ax+By+Cz+D
and P2 = Wx + Xy +Yz +Z
then to intesect in a line... [A,B,C] canot equal k[W,X,Y] k is any num
Anton
Intersecting planes are two or more planes that share a common point or line. This point or line is called the intersection and is where the planes meet.
The easiest way to determine the equations of intersecting planes is by finding the point of intersection and then using that point to solve for the coefficients in the equations of the planes.
Finding the equations of intersecting planes allows us to understand the relationship between the planes and how they intersect. It also allows us to solve problems involving these planes, such as finding the distance between them or the angle of intersection.
Yes, intersecting planes can have multiple points of intersection. If the planes are not parallel, they will intersect at a line. If the planes are parallel, they will intersect at infinitely many points.
Yes, there are various methods for solving problems involving intersecting planes, such as finding the point of intersection, using vectors, or using the distance formula. The method used will depend on the specific problem at hand.