We may solve these equations simultaneously for y and z in terms of t:y=3t-7z=5t-10.If we combine these equations with the equation x=t with which we began our computation, then we see thatx=ty=3t-7z=5t-10are parametric equations for the line of intersection. Solving for t in ...
The above approach can be readily extended to three dimensions. In three or more dimensions, even two lines almost certainly do not intersect; pairs of non-parallel lines that do not intersect are called skew lines. But if an intersection does exist it can be found, as follows. In three d...
上面个位理解错了个Hint啦 因为由(x-13)/3 = (y-6)/2 = (z-0)/1﹐都可以直接看出a=(13 6 0)和v=(3 2 1) 个Hint只不过是说要设法由条件L is the line of intersection beeen the planes x-y-z = 7 and x-2y+z=1.中设法找出a和v罢了。[相反来说﹐若果你已经找到条...
Find the equation of the plane that contains the line (x,y,z)=(1,0,0)+t(1,3,2), and is parallel to the line of intersection of the two planes -x+2y+z=0 and x+z+1=0 Here is what bothers me: my partner found the answer by putting plane 1 and 2 in an augmented matrix...
Via Geometric (Clifford) Algebra: Equation for Line of Intersection of Two PlanesJames A. Smith
Find the distance from the origin to the line of intersection of the two planes: {eq}2x - 3y + z = 5, \; 3x - y - 2z = 11 {/eq}. DIstance To Origin: The equation of the intersection line between two planes is found solving linear systems pr...
Plane Containing a Given Point and the Line of Intersection of Two Planes An equation is found for the plane that contains a given point, and the line of intersection of two given planes. Both an algebraic and a vector solution are given. Note: In Maple 2018, context-sensitive menus were...
A vector parallel to the line of intersection of two planes can be obtained by taking cross products of vectors normal to the planes. Answer and Explanation:1 Write the normal vectors for both the planes: Plane 1: {eq}5y - 2z - 3 = 0 {/eq}. ...
The intersection of two planes is a line. ♦ The part of a line that lies between two points on the line is called a line segment. The American Heritage® Student Science Dictionary, Second Edition. Copyright © 2014 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton ...
Find parametric equations for the line of intersection of the two planes x - 2y + z = 3 and x - y -z = 0. Find parametric equations of the line of intersection of the planes: -x+2y+3z=4 and x+2y-z=4 Find parametric equations of the line of intersect...