Given the following pairs of lines, determine whether they are
parallel, intersecting or skew, if they...
Given the following pairs of lines, determine whether they are
parallel, intersecting or skew, if they intersect, find the
intersecting and the plane containing them.
1) L1: (x-1)/1=(y-2)/1=(z-3)/-2
L2:(x-1)/1=(y-3)/0=(z-2)/-1
2) L1: x=t, y=-t,z=-1 L2: x=s, y=s,
z=5
2) L1: (3+2x)/0=(-3+2y)/1=(6-3z)/2 L2:
x=5/2, y=(3/2)-3t, z=2+4t
Find the distance between the given skew lines x=5-t, y=4+5t,
z=1-3t and x=t, y=9, z=5t
KINDLY...
Find the distance between the given skew lines x=5-t, y=4+5t,
z=1-3t and x=t, y=9, z=5t
KINDLY INCLUDE THE COMPLETE SOLUTION
(a) Find the distance between the skew lines l1 and l2 given
with the vector equations...
(a) Find the distance between the skew lines l1 and l2 given
with the vector equations l1 : r1(t) = (1+t)i+ (1+6t)j+ (2t)k; l2 :
r2(s) = (1+2s)i+ (5+15s)j+ (−2+6s)k.
(b) Determine if the plane given by the Cartesian equation −x +
2z = 0 and the line given by the parametric equations x = 5 + 8t, y
= 2 − t, z = 10 + 4t are orthogonal, parallel, or neither.
Determine whether the lines l1: x = 2 +
u, y = 1 + u, z...
Determine whether the lines l1: x = 2 +
u, y = 1 + u, z = 4 + 7u and
l2: x = -4 + 5w;
y = 2 - 2w, z = 1 - 4w intersect, and if so, find
the point of intersect, and the angles between
the lines.
Find the distance between the skew lines
L1: x = 1 − t , y =...
Find the distance between the skew lines
L1: x = 1 − t , y = 2 t , z = 2 + t
L2: x = -2 + s, y = 3 - s, z = -1 + 2s
Determine whether the lines
L1:→r(t)=〈−2,−1,3〉t+〈−5,−3,−1〉 and
L2:→p(s)=〈4,2,−6〉s+〈4,−1,0〉
intersect. If they do, find the point of intersection.
Determine whether the lines
L1:→r(t)=〈−2,−1,3〉t+〈−5,−3,−1〉 and
L2:→p(s)=〈4,2,−6〉s+〈4,−1,0〉
intersect. If they do, find the point of intersection.
6.(a) Determine whether the lines ?1and ?2 are parallel, skew,
or intersecting. If they intersect, find...
6.(a) Determine whether the lines ?1and ?2 are parallel, skew,
or intersecting. If they intersect, find the point of intersection.
[6 points] ?1: ? = 5 − 12 ?, ? = 3 + 9?, ? = 1 − 3? ?2: ? = 3 + 8?,
? = −6?, ? = 7 + 2?
(b) Find the distance between the given parallel planes. [10
points] 2? − 4? + 6? = 0, 3? − 6? + 9? = 1
At what point do the curves r1 =〈 t
, 1 − t , 3 +...
At what point do the curves r1 =〈 t
, 1 − t , 3 + t2 〉 and r2 =
〈 3 − s , s − 2 , s2 〉 intersect? Find the angle of
intersection.
Determine whether the lines L1 :
r1 = 〈 5 − 12t , 3 + 9t ,1 − 3t 〉 and
L2 : r2 = 〈 3 + 8s , −6s , 7
+ 2s 〉are parallel, skew, or intersecting. Explain. If...
Find the point of intersection of the two lines l1:x⃗
=〈8,6,−16〉+t〈−1,−5,−1〉l1:x→=〈8,6,−16〉+t〈−1,−5,−1〉 and l2:x⃗
=〈21,1,−43〉+t〈3,1,−5〉l2:x→=〈21,1,−43〉+t〈3,1,−5〉
Intersection point:
Find the point of intersection of the two lines l1:x⃗
=〈8,6,−16〉+t〈−1,−5,−1〉l1:x→=〈8,6,−16〉+t〈−1,−5,−1〉 and l2:x⃗
=〈21,1,−43〉+t〈3,1,−5〉l2:x→=〈21,1,−43〉+t〈3,1,−5〉
Intersection point: