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Mathematics
Problem
Let
r
=
a
+
λ
l
r = a + \lambda l
r
=
a
+
λ
l
and
r
=
b
+
μ
m
r = b + \mu m
r
=
b
+
μ
m
be two lines in space, where
a
=
5
i
+
j
+
2
k
a = 5i + j + 2k
a
=
5
i
+
j
+
2
k
,
b
=
−
i
+
7
j
+
8
k
b = -i + 7j + 8k
b
=
−
i
+
7
j
+
8
k
,
l
=
−
4
i
+
j
−
k
l = -4i + j - k
l
=
−
4
i
+
j
−
k
, and
m
=
2
i
−
5
j
−
7
k
m = 2i - 5j - 7k
m
=
2
i
−
5
j
−
7
k
, then the position vector of a point which lies on both of these lines, is a.
i
+
2
j
+
k
i + 2j + k
i
+
2
j
+
k
b.
2
i
+
j
+
k
2i + j + k
2
i
+
j
+
k
c.
i
+
j
+
2
k
i + j + 2k
i
+
j
+
2
k
d. non-existent as the lines are skew
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