Equation of a Plane passing through 3 Non-Collinear points and Equation of plane passing through the Intersection of 2 given Planes

# Equation of a Plane passing through 3 Non-Collinear points and Equation of plane passing through the Intersection of 2 given Planes Video Lecture | Mathematics (Maths) Class 12 - JEE

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

## FAQs on Equation of a Plane passing through 3 Non-Collinear points and 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 three non-collinear points?
Ans. To find the equation of a plane passing through three non-collinear points, you can use the formula: Ax + By + Cz + D = 0 where (x, y, z) are the coordinates of a point on the plane, and A, B, C, and D are constants. Substitute the coordinates of the three non-collinear points into this equation and solve the resulting system of equations to find the values of A, B, C, and D.
 2. How do you determine if three points are non-collinear?
Ans. Three points are considered non-collinear if they do not lie on the same line. To determine if three points are non-collinear, you can calculate the area of the triangle formed by the points. If the area is non-zero, then the points are non-collinear. However, if the area is zero, the points are collinear.
 3. 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, you can use the cross product of the normal vectors of the two planes. Let's say the normal vectors of the given planes are n1 and n2. Then the equation of the plane passing through their intersection is: n1 · (x, y, z) = n1 · P where (x, y, z) are the coordinates of a point on the plane, n1 · (x, y, z) represents the dot product between the normal vector and the coordinates, and P is a point on the intersection of the two planes.
 4. How many points are needed to uniquely determine a plane?
Ans. Three non-collinear points are needed to uniquely determine a plane in three-dimensional space. These three points will not lie on the same line, ensuring that they define a unique plane. Any additional points beyond three will lie on the plane defined by these three points.
 5. Can two planes intersect at a single point?
Ans. Yes, two planes can intersect at a single point. This occurs when the normal vectors of the two planes are not parallel. The intersection of the planes will be a line, and if this line intersects with a third plane, it can result in a single point of intersection. However, it is also possible for the two planes to be parallel or coincide, in which case they will not intersect or intersect along a line, respectively.

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

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