debwaldy said:Hello,so this is prob a v v basic question but I am confused as to how one find the equation of the line of intersection of two planes:e.g. 2x + 3y + 5z = 2 & 4x + 2y + z = 11. is there just one unique solution or will the solution involve parameters??eeks
The question asks for the line at which the two planes intersect. Yes there is a unique line of intersection and, yes, the equation of a line in 3 dimensions involves a parameter!
The intersection line of two planes is the line where the two planes meet or intersect. It is a one-dimensional space that is common to both planes.
To find the intersection line of two planes, you can use the cross product of the normal vectors of the two planes. The resulting vector will be parallel to the intersection line and can be used to find two points on the line. Alternatively, you can also solve the system of equations formed by the equations of the two planes to find the coordinates of the intersection point.
The intersection line represents the points that satisfy the equations of both planes. It is the set of points where the two planes intersect and therefore, it lies on both planes.
Yes, the intersection line of two planes can be parallel if the planes themselves are parallel. In this case, the planes will not intersect and the intersection line will be an empty set.
The normal vectors of two intersecting planes are perpendicular to each other. This means that their dot product is equal to zero. This property is used in finding the intersection line of two planes using the cross product method.