(3)
and
sin θ =
(
)
2
2
2
1
2
2
1
1
2
2
1
1 2
2 1
(
)
(
)
l m
l m
m n
m n
n l
n l
−
−
−
+
− (4)
Two lines with direction ratios a1, b1, c1 and a2, b2, c2 are
(i)
perpendicular i e if θ = 90° by (1)
a1a2 + b1b2 + c1c2 = 0
(ii)
parallel i