Let L1 be the line passing through the point
P1(3, 5, ?5) with direction vector
d=[?1,...
Let L1 be the line passing through the point
P1(3, 5, ?5) with direction vector
d=[?1, 2, 0]T, and let
L2 be the line passing through the point
P2(?3, ?4, ?3) with the same direction
vector.
Find the shortest distance d between these two lines, and
find a point Q1 on L1 and a
point Q2 on L2 so that
d(Q1,Q2) = d. Use
the square root symbol '?' where needed to give an exact value for
your answer.
Let L1 be the line passing through the point
P1=(−5, −2, −5) with direction vector
→d=[2,...
Let L1 be the line passing through the point
P1=(−5, −2, −5) with direction vector
→d=[2, −3, −2]T, and let L2
be the line passing through the point P2=(4,
−1, −5) with the same direction vector.
Find the shortest distance d between these two lines, and
find a point Q1 on L1 and a
point Q2 on L2 so that
d(Q1,Q2) = d. Use
the square root symbol '√' where needed to give an exact value for
your answer.
Let L1 be the line passing through the point
P1(?5, ?3, ?2) with direction vector
d=[0,...
Let L1 be the line passing through the point
P1(?5, ?3, ?2) with direction vector
d=[0, ?3, ?2]T, and let
L2 be the line passing through the point
P2(?2, 3, ?3) with the same direction
vector.
Find the shortest distance d between these two lines, and
find a point Q1 on L1 and a
point Q2 on L2 so that
d(Q1,Q2) = d. Use
the square root symbol '?' where needed to give an exact value for
your answer.
d...
The line l1 has the direction vector h1,0,−1i and passes through
the point (0,−1,−1). The line...
The line l1 has the direction vector h1,0,−1i and passes through
the point (0,−1,−1). The line l2 passes through the points (1,2,3)
and (1,3,2).
a. [2] What is the angle between l1 and l2 in radians? The
answer should lie between 0 and π/2.
b. [6] What is the distance between l1 and l2?
(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.
a) Let T be the plane 3x-y-2z=9. Find the shortest distance d
from the point P0...
a) Let T be the plane 3x-y-2z=9. Find the shortest distance d
from the point P0 = (5, 2, 1) to T, and the point Q in T that is
closest to P0. Use the square root symbol where needed.
d=
Q= ( , , )
b) Find all values of X so that the triangle with vertices A =
(X, 4, 2), B = (3, 2, 0) and C = (2, 0 , -2) has area (5/2).
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:
Find vector and parametric equations for:
a) the line that passes through the point P(9,-9,6) parallel...
Find vector and parametric equations for:
a) the line that passes through the point P(9,-9,6) parallel to
the vector u = <3,4,-2>
b) the line passing through the point P(6,-2,6) parallel to the
line x=2t, y = 2 - 3t, z = 3 +6t
c) the line passing through the point P(5, -2,1) parallel to the
line x = 3 - t, y = -2 +4t, z = 4 + 8t
Find the equation of the line passing through the point (1,2,3)
and perpendicular to the lines...
Find the equation of the line passing through the point (1,2,3)
and perpendicular to the lines r1(t) = (3 - 2t, 5 + 8t,
7 - 4t) and r2(t) = (-2t, 5 + t, 7 - t)