278 COMPUTER AIDED ENGINEERING DESIGN
ΔABC =
201
501
0–41
= –12. Similarly ΔABD = 12, ΔACD= –16 and ΔBCD= – 40
SinceΔABC and ΔABDare of opposite signs, C and D lie on opposite sides of AB. Since ΔACDand
ΔBCDare of same sign, A and B lie on same side of CD. Thus, CD and AB do not intersect (Figure
9.4 (a)).
(b) The determinants ΔABC,ΔABD,ΔACD and ΔBCD are –12, 12, 8 and –16, respectively. Since
ΔABC and ΔABDas well as ΔACDandΔBCDare of opposite signs in pairs, AB and CD intersect
(Figure 9.4 (b)). The parametric equation of AB is x = 2 + t (5 – 2), y = 0 + t (0 – 0), 0 ≤t≤ 1 and
(a) (b) (c)
y
yy
D
D
C D
O A B x O ABx
C
O A B x
C
Figure 9.4 Intersection of lines, Example 9.2.
B
C
D
A
D
B
C
A A
D
C
B
(a) Non-intersecting lines (b) Non-intersecting lines (c) Single point of intersection
BBB
A
C
D D D
C
A C
A
(d) Collinear but not intersecting (e) Collinear and having a (f) Collinear and having a
common end point common segment
Figure 9.3 Intersection of lines