Higher Engineering Mathematics, Sixth Edition
262 Higher Engineering Mathematics R 0 2 27.67 2 6.99 Figure 24.38 Thus, v 2 −v 1 −v 3 =28.54 units at 194. 18 ◦ This result ...
Vectors 263 From the geometry of the vector triangle, the magnitudeofpq= √ 452 + 552 = 71 .06km/h and the direction ofpq=tan−^1 ...
264 Higher Engineering Mathematics (a)−r (b) 3p (c) 2p+ 3 q (d)−p+ 2 r (e) 0. 2 p+ 0. 6 q− 3. 2 r (a) −r=−(− 3 i+ 5 j− 4 k)=+ 3 ...
Chapter 25 Methods of adding alternating waveforms 25.1 Combination of two periodic functions There are a number of instances in ...
266 Higher Engineering Mathematics amplitude, of the resultant is 3.6. The resultant wave- formleadsy 1 =3sinAby34◦or34× π 180 r ...
Methods of adding alternating waveforms 267 Hence, the sinusoidal expression forthe resultanti 1 +i 2 is given by: iR=i 1 +i 2 = ...
268 Higher Engineering Mathematics Problem 5. Two alternating currents are given by:i 1 =20sinωtamperes and i 2 =10sin ( ωt+ π 3 ...
Methods of adding alternating waveforms 269 y 155 /6 or 30 8 y 254 Figure 25.12 y 155 y 25 4 (^0) yR a b 308 Figure 25.13 Usi ...
270 Higher Engineering Mathematics Hence, by cosine and sine rules, iR=i 1 +i 2 = 26 .46sin(ωt+ 0. (^333) )A Now try the followi ...
Methods of adding alternating waveforms 271 v 15 15 V (a) (b) v 25 25 V /6 or 30 8 0 vR v 2 v 1 1508 308 ab c Figure 25.17 Th ...
272 Higher Engineering Mathematics The voltage drops across two compo- nents when connected in series across an a.c. supply are ...
Methods of adding alternating waveforms 273 v 15 15 V v 1 v 25 25 V vR /6 or 30 8 1508 (a) (b) Figure 25.22 In polar form,vR= ...
274 Higher Engineering Mathematics Hence,v 2 =v−v 1 =30sin100πt −20sin( 100 πt− 0. 59 ) = 30 ∠ 0 − 20 ∠− 0 .59rad =( 30 +j 0 )−( ...
Chapter 26 Scalar and vector products 26.1 The unit triad When a vectorxof magnitudexunits and directionθ◦ is divided by the mag ...
276 Higher Engineering Mathematics 26.2 The scalar product of two vectors When vectoroais multipliedby a scalar quantity,sayk, t ...
Scalar and vector products 277 Let a=a 1 i+a 2 j+a 3 k and b=b 1 i+b 2 j+b 3 k a•b=(a 1 i+a 2 j+a 3 k)•(b 1 i+b 2 j+b 3 k) Multi ...
278 Higher Engineering Mathematics (i) From equation (2), if p=a 1 i+a 2 j+a 3 k and q=b 1 i+b 2 j+b 3 k then p•q=a 1 b 1 +a 2 b ...
Scalar and vector products 279 The direction cosines are: cosα= x √ x^2 +y^2 +z^2 = 3 √ 14 =0.802 cosβ= y √ x^2 +y^2 +z^2 = 2 √ ...
280 Higher Engineering Mathematics Find the angle between the velocity vectors υ 1 = 5 i+ 2 j+ 7 kandυ 2 = 4 i+j−k. [66.40◦] Ca ...
Scalar and vector products 281 Squaring both sides of a vector product equation gives: (|a×b|)^2 =a^2 b^2 sin^2 θ=a^2 b^2 ( 1 −c ...
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