Intersection of a plane with 3-d figures for Grade XII of Karnataka state board syllabus:
Some interesting points are there related to Intersection of a plane.
• If there are three collinear points then there is only one plane that consists of all three points.
• If two different planes have a common point then definitely the intersection of those planes would be a line.
• Two planes would be parallel if they have no common points or they are identical.
• A plane section of a 3D figure would be an intersection of that figure with a plane.
• If a line l is perpendicular to two different lines m and n at their point of intersection then that line(l) would be perpendicular to the plane that contains those lines(m and n).
In 3D coordinate system a point is defined with the three coordinates which indicates its position from the all three axes. There are three coordinate systems
• Cartesian coordinate system
• Cylindrical coordinate system
• Spherical coordinate system
You can also improve your math skills by reading Parallel and Perpendicular Planes. In Cartesian coordinate system appoint P is denoted as P(x, y, z). The three axes in all three coordinate systems are perpendicular to each other.
In cylindrical coordinate system a point P is denoted by the points P(r, ᶲ, z). for ex ample we can choose a ray originating at the intersection at the plane and the axis( the origin). Here r is the radius of the cylinder, ᶲ is the angle between x axis and the cylinder’s radius and z denotes the z coordinate.
For transforming cylindrical coordinates to Cartesian coordinates or vice versa transform equations are used.
X = r cos θ; y = r sin θ and z = z. Visit this for more information.
Spherical coordinates are denoted as P(r, θ, ᶲ). The same for transition of one form to other transition equations are needed.
In upcoming posts we will discuss about Learn Pythagorean Theorem and quartiles. Visit our website for information on Binomial Probability
Some interesting points are there related to Intersection of a plane.
• If there are three collinear points then there is only one plane that consists of all three points.
• If two different planes have a common point then definitely the intersection of those planes would be a line.
• Two planes would be parallel if they have no common points or they are identical.
• A plane section of a 3D figure would be an intersection of that figure with a plane.
• If a line l is perpendicular to two different lines m and n at their point of intersection then that line(l) would be perpendicular to the plane that contains those lines(m and n).
In 3D coordinate system a point is defined with the three coordinates which indicates its position from the all three axes. There are three coordinate systems
• Cartesian coordinate system
• Cylindrical coordinate system
• Spherical coordinate system
You can also improve your math skills by reading Parallel and Perpendicular Planes. In Cartesian coordinate system appoint P is denoted as P(x, y, z). The three axes in all three coordinate systems are perpendicular to each other.
In cylindrical coordinate system a point P is denoted by the points P(r, ᶲ, z). for ex ample we can choose a ray originating at the intersection at the plane and the axis( the origin). Here r is the radius of the cylinder, ᶲ is the angle between x axis and the cylinder’s radius and z denotes the z coordinate.
For transforming cylindrical coordinates to Cartesian coordinates or vice versa transform equations are used.
X = r cos θ; y = r sin θ and z = z. Visit this for more information.
Spherical coordinates are denoted as P(r, θ, ᶲ). The same for transition of one form to other transition equations are needed.
In upcoming posts we will discuss about Learn Pythagorean Theorem and quartiles. Visit our website for information on Binomial Probability
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