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x =-y+2 = -z+2 The symmetric equations for 2 lines in 3-D space are given as:...
56. Let Li and L2 be the lines whose parametric equations are L]: x = 41,...
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...
3. (14 points) Given the lines: 21:2(t) = -3t – 1, y(t) = 2t +4, z(t)...
3. (14 points) Given the lines: 21:2(t) = -3t – 1, y(t) = 2t +4, z(t) =t+4 12: x(u) = 5 - 3u, y(u) = u +1, (u) = u +2 1. Determine whether li and ly are parallel, skew or intersect. If the lines intersect, find the point of intersection of li and 12. 2. If the lines intersect or are parallel, give an equation for the plane which contains both lines. If the lines are skew, find a...
1) Show that two lines are skew x+1 y+2 z+3 4:x=y=z and L: +7=5 2) Find...
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.
Given two lines in space, either they are parallel, they intersect, or they are skew (lie in parallel planes). Dete...
Given two lines in space, either they are parallel, they
intersect, or they are skew (lie in parallel planes). Determine
whether the lines below, taken two at a time, are parallel,
intersect, or are skew. If they intersect, find the point of
intersection. Otherwise, find the distance between the two
lines.
12.5.65 Question Help Given two lines in space, either they are parallel, they intersect, or they are skew (lie in parallel planes). Determine whether the lines below, taken two...
Given two lines in space, either they are parallel, they intersect, or they are skew (lie in para...
The same question but has 3 parts
Given two lines in space, either they are parallel, they intersect, or they are skew (lie in parallel planes). Determine whether the lines below, taken two at a time, are parallel, intersect, or are skew. If they intersect, find the point of intersection. Otherwise, find the distance between the two lines. Select the correct choice below and fill in the answer box(es) to complete your choice. Type exact answers, using radicals as needed.)...
(a). Find the equation of the plane through Po = (1,2,1) with normal vector i =...
(a). Find the equation of the plane through Po = (1,2,1) with normal vector i = (3,1,2) (b). Find the equation of a plane through Po = (2,3,1) and parallel to the plane P:3x + 2y -- z = 4 | Q4. Consider the line z-3 y-2 3 L, : * - - - L2: **** 2+5 y-3 -1 2 (i). Write the equations of both lines in parametric form (ii). Find the direction vectors V1, V2 of the lines...
Calculate the distance between the lines L1 : x = −4+7t, y = −4+6t, z =...
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 = ?
Find the plane determined by the intersecting lines. L1 x= -1 +41 y=2+t z= 1 -...
Find the plane determined by the intersecting lines. L1 x= -1 +41 y=2+t z= 1 - 4 L2 x = 1 - 4s y= 1 + 25 z=2-2s The equation of the plane is (Type an equation.)
QUESTION 1 (15 MARKS) a) Given the line Lj: I = 2 - 2t, y =...
QUESTION 1 (15 MARKS) a) Given the line Lj: I = 2 - 2t, y = 5 + 2t, z=t-1 and 1 1 - 2 L2 : =y-3 = 2 4 i. Check whether the lines Lị and L2 parallel, intersect or skewed? (5 marks) ii. Find the shortest distance from the point (1, 2, -1) to the line Li- (3 marks) b) Given two planes 71 : 20 - 4y +z = 5 and T2 : 7x + y...
(1) (a) Find the equation of the line, Li, which passes through the points A :...
(1) (a) Find the equation of the line, Li, which passes through the points A : (4,y,z) = (0, -5, -3) and B : (x, y, z)=(3, 1,0). (b) Find the equation of the line, Ly, which passes through the points C:(x, y, z)=(-1, -3,2) and D: (x,y,z) = (4,3,6). (c) Show that L and Ly are not parallel lines. (d) Write the parametric equations for L, and L2, and then show that the lines Li and L2 do not...
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...
3. (14 points) Given the lines: 21:2(t) = -3t – 1, y(t) = 2t +4, z(t) =t+4 12: x(u) = 5 - 3u, y(u) = u +1, (u) = u +2 1. Determine whether li and ly are parallel, skew or intersect. If the lines intersect, find the point of intersection of li and 12. 2. If the lines intersect or are parallel, give an equation for the plane which contains both lines. If the lines are skew, find a...
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.
Given two lines in space, either they are parallel, they
intersect, or they are skew (lie in parallel planes). Determine
whether the lines below, taken two at a time, are parallel,
intersect, or are skew. If they intersect, find the point of
intersection. Otherwise, find the distance between the two
lines.
12.5.65 Question Help Given two lines in space, either they are parallel, they intersect, or they are skew (lie in parallel planes). Determine whether the lines below, taken two...
The same question but has 3 parts
Given two lines in space, either they are parallel, they intersect, or they are skew (lie in parallel planes). Determine whether the lines below, taken two at a time, are parallel, intersect, or are skew. If they intersect, find the point of intersection. Otherwise, find the distance between the two lines. Select the correct choice below and fill in the answer box(es) to complete your choice. Type exact answers, using radicals as needed.)...
(a). Find the equation of the plane through Po = (1,2,1) with normal vector i = (3,1,2) (b). Find the equation of a plane through Po = (2,3,1) and parallel to the plane P:3x + 2y -- z = 4 | Q4. Consider the line z-3 y-2 3 L, : * - - - L2: **** 2+5 y-3 -1 2 (i). Write the equations of both lines in parametric form (ii). Find the direction vectors V1, V2 of the lines...
Find the plane determined by the intersecting lines. L1 x= -1 +41 y=2+t z= 1 - 4 L2 x = 1 - 4s y= 1 + 25 z=2-2s The equation of the plane is (Type an equation.)
QUESTION 1 (15 MARKS) a) Given the line Lj: I = 2 - 2t, y = 5 + 2t, z=t-1 and 1 1 - 2 L2 : =y-3 = 2 4 i. Check whether the lines Lị and L2 parallel, intersect or skewed? (5 marks) ii. Find the shortest distance from the point (1, 2, -1) to the line Li- (3 marks) b) Given two planes 71 : 20 - 4y +z = 5 and T2 : 7x + y...
(1) (a) Find the equation of the line, Li, which passes through the points A : (4,y,z) = (0, -5, -3) and B : (x, y, z)=(3, 1,0). (b) Find the equation of the line, Ly, which passes through the points C:(x, y, z)=(-1, -3,2) and D: (x,y,z) = (4,3,6). (c) Show that L and Ly are not parallel lines. (d) Write the parametric equations for L, and L2, and then show that the lines Li and L2 do not...
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