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Examples : Equation of a Plane passing through 3 Non-Collinear points Video Lecture | Mathematics (Maths) Class 12 - JEE
FAQs on Examples : Equation of a Plane passing through 3 Non-Collinear points Video Lecture - Mathematics (Maths) Class 12 - JEE
| 1. What is the equation of a plane passing through three non-collinear points? |  |
Ans. The equation of a plane passing through three non-collinear points, P1(x1, y1, z1), P2(x2, y2, z2), and P3(x3, y3, z3), can be found using the formula:
A(x - x1) + B(y - y1) + C(z - z1) = 0, where A, B, and C are the coefficients of the equation and can be calculated using the cross product of the vectors formed by the given points.
| 2. How do you find the coefficients A, B, and C for the equation of a plane? | |
Ans. To find the coefficients A, B, and C for the equation of a plane passing through three non-collinear points, you can use the cross product of the vectors formed by the given points.
Let's say the vectors are v1 = P2 - P1 and v2 = P3 - P1. Then, the coefficients A, B, and C can be calculated as follows:
A = (y2 - y1)(z3 - z1) - (z2 - z1)(y3 - y1)
B = (z2 - z1)(x3 - x1) - (x2 - x1)(z3 - z1)
C = (x2 - x1)(y3 - y1) - (y2 - y1)(x3 - x1)
| 3. Can a plane equation have multiple solutions passing through the same three points? | |
Ans. No, a plane equation passing through three non-collinear points will have a unique solution. Since the three points are not on the same line (non-collinear), they uniquely determine a plane. Thus, the equation of the plane passing through these points will be unique.
| 4. Is it possible for three collinear points to have an equation of a plane passing through them? | |
Ans. No, it is not possible for three collinear points to have an equation of a plane passing through them. Collinear points lie on the same line, and a plane is a two-dimensional surface. To determine a unique plane, we need three non-collinear points that are not in a straight line.
| 5. What is the significance of finding the equation of a plane passing through three points? | |
Ans. Finding the equation of a plane passing through three non-collinear points is significant in various fields such as geometry, engineering, and physics. It helps in understanding the spatial relationship between the points and provides a mathematical representation of the plane. This equation can be used for further calculations, such as determining distances, angles, or intersections with other objects in the 3D space.
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