The two given planes are
As the above two equations have 3 variables, we can assume a free variable.
Let y = t. Then,
From (1), we get
Substituting the above value of x in (2), we get
Now,
Hence, the line of intersection of the two given planes is
Find the line of intersection of the planes x + 2y + z = 7 and x - 2y + 3z = 13. x = 4t+4, y = t and z = 2t + 3 x=-4t+4, y = t and z= 2t-3 x=-4t+ 7, y=t and z= 2t + 3 x=-4t +4, y = t and z = 2t + 3
Find the line of intersection of the planes x + 3y + z = 5 and x - 5y + 3z = 11. O x = -7t + 5, y = t and z = 4t + 3 x= 7t+2, y=t and z = 4t + 3 x=-7t + 2, y = t and z = 4t+ 3 x=-7t+2, y = t and z = 4t - 3
Find the equation of the plane through the line of intersection of the planes x-z = 3 and y+3z = 4 and perpendicular to the plane x+y+z = 1.
Question 12 Find parametric equations for the line of intersection of the planes - 2y+z= 1 and 2x + y - 3x = -3. Does the line L intersect the plane 2x - y - 3x = 1? If so, at what point? Note: This is the review exercise at the end of Lecture 2.
Find a plane containing the point (2,3,−1) and the line of intersection of the planes 2x+y-2z=22 and x+2y+3z=-14 The equation of the plane is
Find the equation of the line in symmetric form that is the intersection of the planes: 3x-y+z=6 2x+y+3z=14
Find the the line of intersection of the two planes 3x - 2y + z=1 2x+4-32=3
1. (10 points) Find an equation of the line of intersection of the planes 2 + 2y +32 = 2 2 + y + z = 1
Consider the following planes. x + y + z = 1, x + 5y + 5z = 1 (a) Find parametric equations for the line of intersection of the planes. (Use the parameter t.) (X(t), y(t), z(t)) = ( 1, – 4t, 4t (b) Find the angle between the planes. (Round your answer to one decimal place.) 10.7 Xo
3. Find two different planes whose intersection is the line x = 1+t, y = 2-4,3 + 2t. Show work.