FAQs on Examples: Equation of plane Passing through the Intersection of 2 given Planes

Question 1

1. What is the equation of a plane passing through the intersection of two given planes?

Accepted Answer

Ans. To find the equation of a plane passing through the intersection of two given planes, we can use the cross product of the normal vectors of the given planes.

Question 2

2. How do you determine the normal vectors of two given planes?

Accepted Answer

Ans. The normal vectors of two given planes can be determined by taking the coefficients of the x, y, and z terms in the equations of the planes. These coefficients represent the direction perpendicular to the planes.

Question 3

3. Can the equation of a plane passing through the intersection of two given planes have multiple solutions?

Accepted Answer

Ans. No, the equation of a plane passing through the intersection of two given planes will have a unique solution. The intersection of two planes forms a line, and the equation of the plane passing through this line will be determined by the cross product of the normal vectors.

Question 4

4. What if the two given planes are parallel? Can a plane still pass through their intersection?

Accepted Answer

Ans. If the two given planes are parallel, they do not intersect, and therefore, a plane cannot pass through their intersection. In this case, there is no unique solution for the equation of a plane passing through the intersection.

Question 5

5. Are there any special cases where the equation of a plane passing through the intersection of two given planes does not exist?

Accepted Answer

Ans. Yes, if the two given planes are coincident (i.e., they are the same plane), then the equation of a plane passing through their intersection does not exist. This is because their intersection is not a line, but rather the entire plane itself.

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