Question

Are lines L1 and L2 perpendicular: L1 (-7,1) and (5,-2) L2 (3,7) and (0,-5) a.) No, the lines are not perpendicular because the product of their slope equals -1. B.) Yes , the lines are perpendicular because the product of their slopes does not equal -1. C.) No, the lines are not perpendicular because the product of their slopes does not equal -1. D.) Yes, the lines are perpendicular because the product of their slope equals -1.

Answer #1

The given lines are L1 (-7,1) and (5,-2) L2 (3,7) and (0,-5)

WE know that slope of a line passing through two points (x1,y1) and (x2,y2) is

m=(y2-y1)/(x2-x1)

The line L1 through two points (-7,1) and (5,-2)

So the slope is m1=(-2-1)/(5-(-7))

= (-3)/12

= -1/4

The line L2 is through points (3,7) and (0,-5) so the slope is

m2 = (-5-7)/(0-3) = (-12)/(-3)

= 4

Since m1* m2 = (-1/4)*4

=-1

So the lines are perpendicular as the product of their slope is -1

Therefore option D is correct

(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.

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:

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...

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.

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 ℙ1[0, 1] be the set of non-vertical lines (y = mx + b)
restricted to [0, 1], with usual function
addition and scalar multiplication, and define the inner
product:
< ? | ? > = ∫ ?? ?? 1
0 .
A) Find the length (using this inner product) of an arbitrary
line y = mx + b.
B) Find the angle between L1: y = x + 2 and L2: y = 4 –
x.
C) Find the...

Find the line determined by the intersecting lines.
L1: x=-1+3t y=2+t z=1-2t
L2: x=1-4s y=1+2s z=2-2s

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.

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.

Let L1 be the line passing through the point
P1(?5, ?4, 5) with direction vector
d=[?1, 1, 3]T, and let
L2 be the line passing through the point
P2(4, 1, ?4) 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=?...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 6 minutes ago

asked 49 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago

asked 4 hours ago