(1)
But
l2 + m 2 + n2 = 1
Therefore
k2 (a2 + b2 + c2) = 1
or
k =
2
2
2
1
a
b
c
±
+
+
Fig 11 1
© NCERT
not to be republished
THREE D IMENSIONAL G EOMETRY
465
Hence, from (1), the d c ’s of the line are
2
2
2
2
2
2
2
2
2
,
,
a
b
c
l
m
n
a
b
c
a
b
c
a
b
c
=±
= ±
= ±
+
+
+
+
+
+
where, depending on the desired sign of k, either a positive or a negative sign is to be
taken for l, m and n