Consider the lines in space whose parametric equations are as
follows
line #1 x=2+3t, y=3-t, z=2t...
Consider the lines in space whose parametric equations are as
follows
line #1 x=2+3t, y=3-t, z=2t
line #2 x=6-4s, y=2+s, z=s-1
a Find the point where the lines intersect.
b Compute the angle formed between the two lines.
c Compute the equation for the plane that contains these two
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:x=7+3t, y=7+3t, z=−1+t
and
L2:x=−10+4t, y=−12+5t, z=−12+4t
intersect, are skew, or are...
Determine whether the lines
L1:x=7+3t, y=7+3t, z=−1+t
and
L2:x=−10+4t, y=−12+5t, z=−12+4t
intersect, are skew, or are parallel. If they intersect,
determine the point of intersection; if not leave the remaining
answer blanks empty.
(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.
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
Determine how the following lines interact.
(x, y, z) = (-2, 1, 3) + t(1, -1,...
Determine how the following lines interact.
(x, y, z) = (-2, 1, 3) + t(1, -1, 5) ; (x, y, z) =
(-3, 0, 2) + s(-1, 2, -3)
(x, y, z) = (1, 2, 0) + t(1, 1, -1) ; (x, y, z) =
(3, 4, -1) + s(2, 2, -2)
x = 2 + t, y = -1 + 2t, z = -1 – t ; x = -1 - 2s,
y = -1 -1s, z = 1...
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.
Consider plane P: 4x -y + 2z = 8, line: <x, y, z> =
<1+t, -1+2t,...
Consider plane P: 4x -y + 2z = 8, line: <x, y, z> =
<1+t, -1+2t, 3t>, and point Q(2,-1,3)
b) Find the perpendicular distance between point Q and plane
P