Computer Aided Engineering Design

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