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Examples: Equation of plane Passing through the Intersection of 2 given Planes Video Lecture | Mathematics (Maths) Class 12 - JEE
FAQs on Examples: Equation of plane Passing through the Intersection of 2 given Planes Video Lecture - Mathematics (Maths) Class 12 - JEE
| 1. What is the equation of a plane passing through the intersection of two given planes? |  |
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.
| 2. How do you determine the normal vectors of two given planes? | |
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.
| 3. Can the equation of a plane passing through the intersection of two given planes have multiple solutions? | |
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.
| 4. What if the two given planes are parallel? Can a plane still pass through their intersection? | |
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.
| 5. Are there any special cases where the equation of a plane passing through the intersection of two given planes does not exist? | |
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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