Understanding Engineering Mathematics

Motivation

You may need the material of this chapter for:

• the study of structures – from molecular and crystalline to ‘big’ engineering


• computer aided design


• problems in statics


• coordinate geometry (Chapter 7)


• vector algebra and its applications (Chapter 11)


• applications in differentiation and integration (Chapters 8, 9, 10)

5.1 Review

5.1.1 Division of a line in a given ratio ➤147 160➤➤

A lineABof length 30 cm is divided internally by a pointPin the ratio 3 : 2. Find the
lengths ofAPandPB. Repeat for the case whenP dividesABexternally in the same
ratio.

5.1.2 Intersecting and parallel lines and angular measurement
➤148 160➤➤

A.Give the angles in (a) degrees (b) radians corresponding to the following fractions of
a full revolution

(i)

1

2

(ii)

1

3

(iii)

1

4

(iv)

1

12

(v)

3

4

(vi)

5

8

B. Ifl 1 ,l 2 are straight lines, name and evaluate the missing angles.

a 40 °

b c

l 1

l 2

Figure 5.1