3 and the planes Consider the point p = (2, 4,0) in R El. Ez given...
Can you Please answer these questions Multi Variable Calc 23. Parameterize the line of intersection of the planes 3y-22-4 and 61 2y +32-2. 25. Find a Cartesian equation for the plane conatining the line C(t) (2 t, 3 + 2t,t),-oo < t < oo and perpendicular to the plane r-y + z 3.
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...
2. Consider the nonlinear plane autonomous system 3 2 satisfying the initial condition (r(0), y(0)) = (4,0). (a) Change to polar coordinates and find the solution r(t) and (t) of the system (b) As t goes to infinity, (x(t). y(t)) will follow the circle trajectory. Find the radius and period of the circle trajectory. (limit behavior of the solution (a)) 2. Consider the nonlinear plane autonomous system 3 2 satisfying the initial condition (r(0), y(0)) = (4,0). (a) Change to...
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...
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...
2. Find the electric field E at P=[0,9, 0] from uniform line charge with charge density pe=28 nç/m around a rectangle in the yz-plane. The four corners of the rectangle are [0,0,-4], [0, 0, 5), [0, 5, 5], [0,5,-4]. (a) Find Ej at P from line charge (1). (b) Find E2 at P from line charge (2). (c) Find Ez at P from line charge (3). (d) Find E4 at P from line charge (4). (e) Find E at P...
please anyone answer all the questions as soon please 2 4 3 3 4 1. Given three points A = (0,–8, 10), B = (2, -5, 11), C = (-4,-9, 7) in R3. (a) Show that these three points are not collinear (not in a straight line). (b) Find the area of the triangle ABC. (c) Find the scalar equation of the plane containing the points A, B and C. (d) Find a point D on the plane such that...
(4) (a) Determine the standard matrix A for the rotation r of R 3 around the z-axis through the angle π/3 counterclockwise. Hint: Use the matrix for the rotation around the origin in R 2 for the xy-plane. (b) Consider the rotation s of R 3 around the line spanned by h 1 2 3 i through the angle π/3 counterclockwise. Find a basis of R 3 for which the matrix [s]B,B is equal to A from (a). (c) Give...
2. (20 points) Consider the point PO 2, 3) and the - 3+1 (a) Show that the point is not on the line (b) Find the shortest distance from the point to the line (e) Find the equation of the line parallel to the given line but that passes through the point P. (d) Suppose that the plane is perpendicular to the line but passes through the point P. Find the equation of the plane.
4. [3/8 Points) DETAILS PREVIOUS ANSWERS SCALCCC4 9.5.013. Consider the line that passes through the point and is parallel to the given vector. (4, -3,6) < 1, 2, -3> (a) Find symmetric equations for the line. 2-6 -(x-4)= 2 3 y +3 (b) Find the points in which the line intersects the coordinate planes. (5 X IX 0) (0,9 X -6 (4 x 0, 4 X) 1 Consider the line that passes through the point and is perpendicular to the...