Please help with these problems.
Please help with these problems. 8. Consider the two planes listed below 2x - y +...
please show work neatly, will rate! thanks Given two planes in space: 2x – y + z = -4 and 5x + 3y - z = 4. Find the angle between these two planes and the symmetric equations of the line of intersection of these two planes.
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...
QUESTION 1 (15 MARKS) a) Given the line Lj: I = 2 - 2t, y = 5 + 2t, z=t-1 and 1 1 - 2 L2 : =y-3 = 2 4 i. Check whether the lines Lị and L2 parallel, intersect or skewed? (5 marks) ii. Find the shortest distance from the point (1, 2, -1) to the line Li- (3 marks) b) Given two planes 71 : 20 - 4y +z = 5 and T2 : 7x + y...
Find a vector parallel to the line of intersection of the two planes 2x - y + z = 1, 3x + y + z = 2.
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
Find the equation for a plane containing 3 points: A(2, 2,1) in the form: ax+by+cz+d = 0 C(0, -2,1). Put the plane equation B(3,1, 0) х — 3 z+2 = y+5 = 2 L: Find the intersection point between 2 lines whose symmetric equations are: 4 х-2 L, : у-2 = z-3 -3 Find the parametric equation for a line that is going through point A(2,4,6) and perpendicular to the plane 5х-3у+2z-4%3D0. Name: x-3y4z 10 Find the distance between 2...
Additional Problems: (HINT: It suffices to consider Just what happens (DX c A. Show by example that (a x b xc* a with i, j and k:) B. Find a vector which is perpendicular to every vector parallel to the plane z+y 0. C. Find the line which is the intersection of the planes x + y 0 and 3y-z = 0. D. Explain why the vectors in the following form describe a plane (where both t and s are...
Problem 1. (33 Points) (a) Consider the following: Are these two planes parallel? If not, find the parametric equation of their line of intersection (b) Describe the set of all points P = (x, y, z) such that the distance from P to the y-axis is twice the distance from P to the zz-plane. (c) Describe the set of all points P (r, y, 2) such that the distance from P to the plane x + 5y-4z = 1 equals...
ILI UU Q3 (8 points) Find general equation of the plane containing the following two lines C: y =24+1 t +3 5+2 and = 24 L : y = -2 25t-1 + Drag and drop your files or Click to browse Q4 (8 points) (a) Find parametric equations of the line passing through the point A(S. -2,9) and perpendicular to the plane 32 - y - 63 + 2 = 0. (b) Find two planes that intersect along the line...
(1 point) Consider following the system in two equations and two variables: 2x + y || IL X – Select all statements below that use linear algebra vocabulary correctly. A. Solution(s) to the system are points in RP. B. The system is a linear combination. C. The system corresponds to two lines. [2 1 51 D. The system is the same as 11 -1 7] E. The system is two lines. F. The solution to the system is the intersection...