Problem #29: [2 marksFind the shortest distance between the following two parallel lines. x = 1...
find the distance between tha following given lines
x = 5 +t, y = -1, z = 8 + 2t x - 2_y - 22+1 -1 4 3
2x2, Problem #2: Find the mass of the solid bounded by the the graphs of y = y = 4, z = 0, and z = 5, in the first octant, if the density at a point P is equal to 8 times the distance to the yz-plane. Problem #2: Enter your answer symbolically, as in these examples
Problem #2: Let y(x) be the solution to the following initial value problem. x4 y' + 5x> y = Inça), x>0, y(1) = 5. Find y(e). Problem #2: O Problem #2: Enter your answer symbolically, as in these examples Just Save Submit Problem #2 for Grading Problem #2 | Attempt #1 | Attempt #2 | Attempt #3 Your Answer: Your Mark:
3. Find the shortest distance from the center of the quadratic surface 9 x2+54 x +4 y-4 y + 36 z+ 108 z + 73 = 0 to the line of intersection of the planes x + y-z = 10 and -x + 4 y + 8 z = 50 (i.e. Find the shortest distance from the point to the orange line below)
3. Find the shortest distance from the center of the quadratic surface 9 x2+54 x +4 y-4...
x =-y+2 = -z+2 The symmetric equations for 2 lines in 3-D space are given as: 1. L,: x-2 = -y+1 = z+1 a) Show that lines L1 and L2 are skew lines. b) Find the distance between these 2 lines x =1-t y=-3+2t passes through the plane x+ y+z-4=0 2. The line Determine the position of the penetration point. a. Find the angle that the line forms with the plane normal vector n. This angle is also known as...
1) (a) Show that the shortest path between two given points in a plane is a straight line, using plane olar coordinates (b) Let the path between two points lie in a 3-D space, and let the coordinates be parameterized by a "time" t, so that x-x(t). У-y (t), and z-z(t). Write the integral to be minimized and the Euler-Lagrange equations. [Hint: It may help, but it's not necessary, to write all of the equations in vector form]. Find the...
Let y(x) be the solution to the following initial value problem. dy dx In x = -2 xy y(1) = 4 Find y(e). Enter your answer symbolically, as in these examples
1. Are £i and C2 skew lines? Explain your answer and find the distance between them if they are skew lines. 3 marks 2. Let S be the region given by S-((z, y) E R: z2 + y2 4,z? + y2-4y2 0,#2 0, y 20} 1 mark (a) Sketch the region S; (b) Consider the change of variables given by u2 , a2 +y-4y. Describe the region S as set in terms of the variables u and v. Call this...
Calculate the distance between the lines L1 : x = −4+7t, y = −4+6t, z = 0+2t and L2 : x = 10+8s, y = −23+8s,z = 8+5s Distance: D = ?
(1 point) Calculate the distance between the lines L := 0+60, y = -2 +6t, z=0+ 5t and L2 : 2 = 8+7s, y = -15 +8s, z= 6 + 8s Distance: D =