1. (10 points) Find an equation of the line of intersection of the planes 2 +...
Q4. (5 points). Find the equation of the plane that passes through the line of intersection of the two planes x - 2y = 3 and y- z = 0 and parallel to the line x = y - 1 = 2+1 Q5. (4 points). Find the distance from the point A(1,2,3) and the line 2+1 y-1 2 Q6. (4 points). Give the name and sketch the surface whose equation is given by x2 + 2y2 – 12y – z...
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 line of intersection of the planes x + 2y + z = 9 and x - 2y + 3z = 13. x = -4t+ 7, y = and z = 2t + 2 x= -4t+9, y = 1 and z = 2t + 2 x = 4t + 7, y = tand z = 2t +2 x = -4t+ 7, y = ? and z = 2t - 2
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.
Find the the line of intersection of the two planes 3x - 2y + z=1 2x+4-32=3
Find the vector equation for the line of intersection of the planes 52 - 5y + z = 2 and 5x + z = -1 =( ,0) +t(-5, r= ).
5. (15 points) Find the line of intersection of the two planes. Show your work. 3x - 2y +1 2x+y - 3x = 3.
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.
3. Consider the two planes, P and P2, where Pi is given by the general equation 2x y+2-5 and P2 passes through the points (0,0,-1), (3,2,4) and (2, 4,5). (a) Find L, the line of intersection of the two planes. (b) Suppose another line, L2, has vector equation (x, y, z) = (8,3,-2) + t2(-2, 1, 1). 6 marks] Find where Land L2 intersect 4 marks 3. Consider the two planes, P and P2, where Pi is given by the...
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