please show work? SCALCCC4 9.5.062. Find the distance between the skew lines with the given parametric...
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...
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...
56. Let Li and L2 be the lines whose parametric equations are L]: x = 41, y = 1 -21, z = 2 + 21 L2: x = 1+1, y = 1-1, Z=-1+ 41 (a) Show that Li and L2 intersect at the point (2,0, 3). (b) Find, to the nearest degree, the acute angle between L and L2 at their intersection. c) Find parametric equations for the line that is perpen- dicular to L, and L2 and passes through...
Determine if each pair of lines are parallel, skew or intersecting. If the lines intersect, find the point of intersection. Otherwise, find the distance between the lines. Then find a point on each line such that the distance between the points is the distance between the lines. Draw a picture, and use vectors instead of distance formulas to find the distance. Line #1 = < -2,2,8> + t< 1,2,2> Line#2 = < 0,1,5 > + t< -2,-4, -4>
7. [-16 Points) DETAILS SCALCCC4 1.7.031. Find parametric equations for the path of a particle that moves around the given circle in the manner described. x2 + (y - 1)2 = 16 (a) Once around clockwise, starting at (4,1). X(t) = (t) = Osts 2017 (b) Four times around counterclockwise, starting at (4,1). x(t) = 4cos(t) (t) = osts (c) Halfway around counterclockwise, starting at (0,5). x(t) = y(t) = osts Need Help? Read it Watch Talk to Tutor
Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = 4 In(t), y = 6/t, z = t4; (0,6, 1) x(t), y(t), z(t) = X
1:34 Find the parametric equations of the line in Rthat passes through the points (2,4, 1) and (-3, -2,-4). (A) x 25t y 6 6 (B) x 2-5t y 4 6t (C) x -3-5t y 4 6t (D) х--2-t y 6-6t y 6-6t (G) x 2 -5t y 4 6 Problem 45
1) Show that two lines are skew x+1 y+2 z+3 4:x=y=z and L: +7=5 2) Find the general equation of the plane containing the point P (1,2,3 ) and L, . 3) Find the point Q-the point of intersection the plane found in 2) and the line L. 4) Find the distance from the point (1,-1,2) to the line Lą.
1. (Sections 2.11,2.12) The parametric equations of three lines are given below: 4 : (x, y, z) = (1,0,0) + (1,0,-1), TER 19 : (x,y, 2) = (1.0.-1) + (0.1, -1), TER 13: (1.7.2) = (1.-1,-1) + (1,1,0), TER Two of these lines intersect. Which two? What is the equation of the plane that they describe? Give full reasons for your answers. 2. (Sections 2.11,2.12) Given the two planes 2-y-z = 0 and r+y-:-1=0. Find a parametric equation for the...
find the distance between tha following given lines x = 5 +t, y = -1, z = 8 + 2t x - 2_y - 22+1 -1 4 3