# Intersection line of two planes

• debwaldy

#### debwaldy

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 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 Can a system of two equations involving three unknowns have a unique solution?

is there just one unique solution or will the solution involve parameters??
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!

In general, you can solve two equations for two unknowns. Here, you can solve for two of the unknowns (say, x and y) in terms of the third (z). Then you can use that third unknown as the parameter.

## What is the intersection line of two planes?

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.

## How do you find the intersection line of two 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.

## What does the intersection line represent?

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.

## Can the intersection line of two planes be parallel?

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.

## What is the relationship between the normal vectors of two intersecting planes?

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.