Question 3 Let F ( x , Y , 2 ) = cy it ( * + 2 cosy ) ] + sing K , where c is a real constant . ( 2 ) Find the value of c such that F is irrotational...

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Question 3Let F ( x , Y , 2 ) = cy it ( * + 2 cosy ) ] + sing K , where c is a real constant .( 2 ) Find the value of c such that F is irrotational .( 5 marks )( b ) With the value of c obtained in ( a ) , determine a potential function ( ( * , Y , 2) such thatVO = F ." ( 10 marks )( C ). With the value of c obtained in ( a ) , evaluate { { . Ar , where Cis the path moving*from a point ( 0 , 0 , 0 ) to ( 1 , It / 2 , IT / 2 ) along a straight line .( 5 marks )Question 4Compute the following integrals using suitable methods .( a ) JJS ( * 2 + 1 2 ) as , where S' is the part of the surface 2 = 9 - 2 x - y lying inside the cylinder : "* 2 + 1 2 = 1 .( 15 marks )"( b ) SSS F . Ads , where { = xt' t Y ] + z k and S' is boundary surface of the region boundedby the cone 2 = 3 ( * 2 + 1 2 ) and the upper half sphere * 2 ty 2 + 2 2 = 8 ( here ~ is theoutward - pointing normal ) .( 15 marks )- END -