Basic Engineering Mathematics, Fifth Edition

Revision Test 12 : Vectors and adding waveforms 287

11. Givena=− 3 i+3j+5k,b= 2 i− 5 j+7kand
    c= 3 i+6j− 4 k, determine the following:(i)− 4 b
    (ii)a+b−c(iii) 5b− 3 a (6)


12. Calculate the magnitude and directionof the resul-
    tant vector of the displacement system shown in
    Figure RT12.4. (9)

7 m

12 m 10 m

308

608

208

Figure RT12. 4

13. The instantaneous values of two alternating volt-
    ages are given by
    v 1 =150sin

(

ωt+

π

3

)

volts

and

v 2 =90sin

(

ωt−

π

6

)

volts

Plot the two voltages on the same axes to scales

of 1cm=50 volts and 1cm=π/6. Obtain a sinu-

soidal expression for the resultant ofv 1 andv 2 in

the formRsin(ωt+α)(a) by adding ordinates at

intervals and (b) by calculation. (15)