Instead, to describe a line, you need to find a parametrization of the line. My Vectors course: https://www.kristakingmath.com/vectors-courseLearn how to find parametric equations that define the line of intersection of two planes. You can find a point (x 0, y … This means an equation in x and y whose solution set is a line in the (x,y) plane. For example: Find an equation for the line that passes through the point (0,1,-1) and is parallel to the line of intersection of the planes 2x + y - 2z = 5 and 3x - 6y - 2z = 7. edit.. Symmetric form of a line … Typically though, to find the angle between two planes, we find the angle between their normal vectors. This leaves you two equations in y and z. You can plot two planes with ContourPlot3D, h = (2 x + y + z) - 1 g = (3 x - 2 y - z) - 5 ContourPlot3D[{h == 0, g == 0}, {x, -5, 5}, {y, -5, 5}, {z, -5, 5}] And the Intersection as a Mesh Function, Two planes always intersect in a line as long as they are not parallel. Basic Equations of Lines and Planes Equation of a Line. How can we obtain a parametrization for the line formed by the intersection of these two planes? In addition to finding the equation of the line of intersection between two planes, we may need to find the angle formed by the intersection of two planes. First we read o the normal vectors of the planes: the normal vector ~n 1 of x 1 5x 2 +3x 3 = 11 is 2 4 1 5 3 3 5, and the normal vector ~n 2 of 3x 1 +2x 2 2x 3 = 7 is 2 4 3 2 2 3 5. Finding the line between two planes can be calculated using a simplified version of the 3-plane intersection algorithm. The 2'nd, "more robust method" from bobobobo's answer references the 3-plane intersection.. It's not is when the normal vectors for both planes are parallel to each other. Thus the line of intersection is. A vector normal to the first plane is . Example: Find a vector equation of the line of intersections of the two planes x 1 5x 2 + 3x 3 = 11 and 3x 1 + 2x 2 2x 3 = 7. Thus a set of n lines can be represented by 2n equations in the 3-dimensional coordinate vector w = (x, y, z) T: = The most popular form in algebra is the "slope-intercept" form. x = x 0 + p, y = y 0 + q, z = z 0 + r. where (x 0, y 0, z 0) is a point on both planes. The intersection line between two planes passes throught the points (1,0,-2) and (1,-2,3) We also know that the point (2,4,-5)is located on the plane,find the equation of the given plan and the equation of another plane with a tilted by 60 degree to the given plane and has the same intersection line given for the first plane. An important topic of high school algebra is "the equation of a line." For example, builders constructing a house need to know the angle where different sections of the roof meet to know whether the … Plane, Plane intersection Typically, this is a line. While this works well for 2 planes (where the 3rd plane can be calculated using the cross product of the first two), the problem can be further reduced for the 2-plane version. Solve for both of these for the point. How does one write an equation for a line in three dimensions? Derive Equation of Plane passing through the intersection of two planes 0 Given a plane and a line, find the equation of another plane that has an angle 30 of degree to the given plane and contains the given line. In three dimensions a line is represented by the intersection of two planes, each of which has an equation of the form () =. the cross product of (a, b, c) and (e, f, g), is in the direction of the line of intersection of the line of intersection of the planes. You should convince yourself that a graph of a single equation cannot be a line in three dimensions. Otherwise, plug in an arbitrary value of x into both planes. y = mx + b. See also Plane-Plane Intersection.