find the shortest distance between two lines y=2x-3 and y=2x+9
Answers
Answer:
L
1
:x−y=0=2x+z and
L
2
:x+y−2=0=3x−y+z−1
It can also be write as
L
1
:
1
x
=
1
y
=
−2
z
L
2
:
−1
x
=
1
y−2
=
4
z−3
A(0,0,0) be the point on L
1
and
B
=(
i
^
+
j
^
−2
k
^
) is a direction of L
1
C(0,2,3) be the point on L
2
and
D
=(−
i
^
+
j
^
+4
k
^
) is a direction of L
2
B
×
D
=6
i
^
−2
j
^
+2
k
^
∣
∣
∣
∣
B
×
D
∣
∣
∣
∣
=
6
2
+2
2
+2
2
=2
11
C
−
A
=2
j
^
+3
k
^
(
B
×
D
).(
C
−
A
)=(6
i
^
−2
j
^
+2
k
^
)⋅(2
j
^
+3
k
^
)=2
The shortest distance between line L
1
and L
2
can bee found using the following formula.
Distance =
∣
∣
∣
∣
∣
∣
∣
B
×
D
∣
B
×
D
.(
C
−
A
)
∣
∣
∣
∣
∣
∣
Distance =
11
1
Answer:
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2 votes
Answer:L 1 :x−y=0=2x+z and L 2 :x+y−2=0=3x−y+z−1It can also be write asL 1 : 1x = 1y = −2z L 2 : −1x = 1y−2 = 4z−3 A(0,0,0) be the point ... More