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Mathematics
Problem
Prove that the two lines whose direction cosines are connected by the two relations
a
l
+
b
m
+
c
n
=
0
al + bm + cn = 0
a
l
+
bm
+
c
n
=
0
and
u
l
2
+
v
m
2
+
w
n
2
=
0
ul^2 + vm^2 + wn^2 = 0
u
l
2
+
v
m
2
+
w
n
2
=
0
are perpendicular if
a
2
(
v
+
w
)
+
b
2
(
w
+
u
)
+
c
2
(
u
+
v
)
=
0
a^2(v + w) + b^2(w + u) + c^2(u + v) = 0
a
2
(
v
+
w
)
+
b
2
(
w
+
u
)
+
c
2
(
u
+
v
)
=
0
and parallel if
a
2
u
+
b
2
v
+
c
2
w
=
0
\frac{a^2}{u} + \frac{b^2}{v} + \frac{c^2}{w} = 0
u
a
2
+
v
b
2
+
w
c
2
=
0
.
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