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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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Oct 23, 2025 Last updated

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	Mathematics (Maths) Class 12 223 videos\|377 docs\|167 tests

Mathematics (Maths) Class 12

223 videos|377 docs|167 tests

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