ch31-p067 - 67. (a) We consider the following combinations:...

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67. (a) We consider the following combinations: V 12 = V 1 V 2 , V 13 = V 1 V 3 , and V 23 = V 2 V 3 . For V 12 , VA t A t A t At dd d d 12 120 2 120 2 2 120 2 36 0 =− ° = ° F H G I K J −° F H G I K J ° sin( ) sin ( ) sin cos cos ωω ω bg where we use ( ) ( ) sin sin 2sin 2 cos 2 αβ α β −= + ⎤⎡ ⎦⎣ and sin 60 3 2. °= Similarly, () 13 2 240 240 sin( ) sin ( 240 ) 2 sin cos 3 cos 120 22 d d t t A t A A t ° ⎛⎞ ∆= ° = = ° ⎜⎟ ⎝⎠ and 23 2 360 120 sin( 120 ) sin ( 240 ) 2 sin cos 3 cos 180 d d t t A t A °
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