Use Lagrange multipliers to find the point on the plane x − 2y + 3z = 6 that is closest to the point (0, 3, 5)
Use lagrange multipliers to find the point on the plane x-2y 3z-14=0 that is closet to the origin?(try and minimize the square of the distance of a point (x,y,z) to the origin subject to the constraint that is on the plane) Help me please!
Find the area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x2 + y2 = 2
Solve 3x + 2y – z = 1x – 2y + z = 02x + y – 3z = -1
TUTTI 1. Find the distance betweenthe two planes. x – 2y + 3z = -4 and x – 2y + 3z = 2.
Solve c and d Please.
Find the area of the following surfaces. a) The part of the plane 3z + 2y +z 6 that lies in the first octant. b) The part of the cone zVy that lies between the plane y z and the cylinder y-x c) The surface with vector equation r(u, u) = (u . cos(v), u . sin(v), u) , where 0 u 1, 0 v S T. d) The portion of the unit sphere that...
Use (part A) line integral directly then use (part B) Stokes'
Theorem
10. Use Stokes's Theorem to evaluate F dr where F(x, y, z) (3z 2y)i + (4x 3y)j + (z + 2y)k and C is the unit circle in the plane z (a) 67 (d) 12m 3. (b) TT (e) None of these (c) 3 TT
10. Use Stokes's Theorem to evaluate F dr where F(x, y, z) (3z 2y)i + (4x 3y)j + (z + 2y)k and C...
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
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...
6. (4 pts) Vectors VÀ and VB generate a square in the plane x +2y + 3z = 1, as shown in the left figure. A smooth vector field F in the square behaves as shown in the right figure. В ID 18 12 10 0 B 10 14 16 18 А Assume that the greatest circulation density of T at P is 5 and at Q is 2. (a) Find curl at P. (b) Find curlī at Q. (c)...