Distance from the point D to the plane ABC Distance from the point A to the straight line BC Distance between the straight lines BC and AD
Distance from the point D to the plane ABC Distance from the point A to the straight line BC Distance between the straight lines BC and AD
Homework Answers
Given four points A = (1, 2, -1), B = (3,2,0), C = (0,1,1) and D=...
Given four points A = (1, 2, -1), B = (3,2,0), C = (0,1,1) and D= (1,0,1). (a) Determine the parametric equations of the line that passes through A and B and of the line that passes through C and D. (b) Determine if the line that passes through A and B intersects with the line that passes through C and D. (c) Determine the distance between the lines in part (a). (d) Determine the equation of a plane that...
Find the equation for a plane containing 3 points: A(2, 2,1) in the form: ax+by+cz+d =...
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...
2. Three cables are attached at point B on the boom of a large construction crane as shown in the...
2. Three cables are attached at point B on the boom of a large construction crane as shown in the figure below. The cable forces acting at point B are FBc 50 kN FBD-100 kN and FBA-75 kN. Determine: a) The resultant, R, of the three (3) forces acting at B, b) The moment of R about the point A, c) The moment of R about the line AD d) The perpendicular distance from A to the line of action...
x =-y+2 = -z+2 The symmetric equations for 2 lines in 3-D space are given as:...
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...
please solve 3 and 4 TEN C hQuestione Each questio n s (A) (0) (C) and...
please solve 3 and 4
TEN C hQuestione Each questio n s (A) (0) (C) and (D) out of whid ONLY ONE Lot L be the line belonging to the family of the straight lines ( 20% - a-b a be which farthest from the point (22) Area formed by the line L with coordinates A) 4/3 units (0) 92 units e) 49/8 sq unite (0) None of these A variable in Lis drawn through 10.) to meet the lines...
2. (20 points) Consider the point PO 2, 3) and the - 3+1 (a) Show that...
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.
(7) Let 0くa 〈 b 〈 c 〈 d for a,b,c,d R. Consider the set and let D be the region in the r-y plance that is the image...
(7) Let 0くa 〈 b 〈 c 〈 d for a,b,c,d R. Consider the set and let D be the region in the r-y plance that is the image of S under the variable transformation (a) Sketch D in the x-y plane for the case ad - bc > 0. (a) Sketch D in the z-y plane for the case ad-bc 〈 0. (c) Calculate the area of D. Show all working.
(7) Let 0くa 〈 b 〈 c 〈...
28 Consider (O:OAOB) an orthonormal system in space. Let G be the center of gravity of triangle ABC. 1° Calculate the coordinates of G 2°Consider the points A' (2 ;0:0) ,B, (0:2:0) and C"...
28 Consider (O:OAOB) an orthonormal system in space. Let G be the center of gravity of triangle ABC. 1° Calculate the coordinates of G 2°Consider the points A' (2 ;0:0) ,B, (0:2:0) and C" (0:0,3). a) Verify that these three points define a plane. b) Write a system of parametric equations of the plane (A'BC'). 3 Write a system of parametric equations of line (AC). 4° Verify that K (4:0-3) is the trace of the line (AC) with the plane...
Question 1 (1 point) A line segment AD, contains points B & C such that C...
Question 1 (1 point) A line segment AD, contains points B & C such that C is between A and D, and B is between A and C. If AB- 6, BD- 23, and AB -CD, find the length of segment BC. 17 23 29 Not enough information to solve the problem
hlep me these 2 t, 3- 3 and (-2r, 3-, ) 11.) Determine the point of...
hlep me these
2 t, 3- 3 and (-2r, 3-, ) 11.) Determine the point of intersection of the lines Note:4,1,2, with (1,2/3,-1)^k(-2.-1,1)=kv;, for any kER. So .1,. Change one of the parameters to s, then equate the corresponding coordinates of the lines and solve for t, and s. substitute the values of t, and s in their respective lines to get the required point. Locate the point of intersection of the plane 2x+ y-z-0 and the line through (3,1,0)...
Given four points A = (1, 2, -1), B = (3,2,0), C = (0,1,1) and D= (1,0,1). (a) Determine the parametric equations of the line that passes through A and B and of the line that passes through C and D. (b) Determine if the line that passes through A and B intersects with the line that passes through C and D. (c) Determine the distance between the lines in part (a). (d) Determine the equation of a plane that...
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...
2. Three cables are attached at point B on the boom of a large construction crane as shown in the figure below. The cable forces acting at point B are FBc 50 kN FBD-100 kN and FBA-75 kN. Determine: a) The resultant, R, of the three (3) forces acting at B, b) The moment of R about the point A, c) The moment of R about the line AD d) The perpendicular distance from A to the line of action...
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...
please solve 3 and 4
TEN C hQuestione Each questio n s (A) (0) (C) and (D) out of whid ONLY ONE Lot L be the line belonging to the family of the straight lines ( 20% - a-b a be which farthest from the point (22) Area formed by the line L with coordinates A) 4/3 units (0) 92 units e) 49/8 sq unite (0) None of these A variable in Lis drawn through 10.) to meet the lines...
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.
(7) Let 0くa 〈 b 〈 c 〈 d for a,b,c,d R. Consider the set and let D be the region in the r-y plance that is the image of S under the variable transformation (a) Sketch D in the x-y plane for the case ad - bc > 0. (a) Sketch D in the z-y plane for the case ad-bc 〈 0. (c) Calculate the area of D. Show all working.
(7) Let 0くa 〈 b 〈 c 〈...
28 Consider (O:OAOB) an orthonormal system in space. Let G be the center of gravity of triangle ABC. 1° Calculate the coordinates of G 2°Consider the points A' (2 ;0:0) ,B, (0:2:0) and C" (0:0,3). a) Verify that these three points define a plane. b) Write a system of parametric equations of the plane (A'BC'). 3 Write a system of parametric equations of line (AC). 4° Verify that K (4:0-3) is the trace of the line (AC) with the plane...
Question 1 (1 point) A line segment AD, contains points B & C such that C is between A and D, and B is between A and C. If AB- 6, BD- 23, and AB -CD, find the length of segment BC. 17 23 29 Not enough information to solve the problem
hlep me these
2 t, 3- 3 and (-2r, 3-, ) 11.) Determine the point of intersection of the lines Note:4,1,2, with (1,2/3,-1)^k(-2.-1,1)=kv;, for any kER. So .1,. Change one of the parameters to s, then equate the corresponding coordinates of the lines and solve for t, and s. substitute the values of t, and s in their respective lines to get the required point. Locate the point of intersection of the plane 2x+ y-z-0 and the line through (3,1,0)...
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