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Mathematics
Problem
Consider the following 3 lines in space
L
1
:
r
=
3
i
−
j
+
2
k
+
λ
(
2
i
+
4
j
−
k
)
L_1: r = 3i - j + 2k + \lambda(2i + 4j - k)
L
1
:
r
=
3
i
−
j
+
2
k
+
λ
(
2
i
+
4
j
−
k
)
L
2
:
r
=
i
+
j
−
3
k
+
μ
(
4
i
+
2
j
+
4
k
)
L_2: r = i + j - 3k + \mu(4i + 2j + 4k)
L
2
:
r
=
i
+
j
−
3
k
+
μ
(
4
i
+
2
j
+
4
k
)
L
3
:
r
=
3
i
+
2
j
−
2
k
+
t
(
2
i
+
j
+
2
k
)
L_3: r = 3i + 2j - 2k + t(2i + j + 2k)
L
3
:
r
=
3
i
+
2
j
−
2
k
+
t
(
2
i
+
j
+
2
k
)
Then, which one of the following pair(s) is/are in the same plane ? a. Only
L
1
L
2
L_1 L_2
L
1
L
2
b. Only
L
2
L
3
L_2 L_3
L
2
L
3
c. Only
L
3
L
1
L_3 L_1
L
3
L
1
d.
L
1
L
2
L_1 L_2
L
1
L
2
and
L
2
L
3
L_2 L_3
L
2
L
3
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