quizbmarkscheme123 - Math2061 Vector Calculus Quiz Version...

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Unformatted text preview: Math2061 Vector Calculus Quiz Version B Solutions 1. (a) 2 marks for correct sketch r ( t ) = 7 i + 6 j + t ( 3 i 5 j ) , (2 marks) Also correct is x = 7 3 t, y = 6 5 t, t 1 (1 mark) (b) 2 marks for correct sketch x = t, y = t 3 (1 mark) 2 t 1 (c) 2 marks for correct sketch x = 4 cos t, y = 4 sin t (1 mark) t 2 (1 mark) 2. (a) contintegraltext C F n ds = contintegraltext C ((3 x + z ) i + y 2 j + (2 z + x ) k ) ( x i + y j ) ds = contintegraltext C ((3 x + z ) i + y 2 j ) ( x i + y j ) ds = integraltext integraltext R ( x (3 x + z ) + y ( y 2 )) dA (1 mark) = integraltext integraltext R (3 + 2 y ) dA (1 mark) = integraltext 2 ( integraltext 1 (3 + 2 r sin rdr ) d (1 mark) = integraltext 2 ( integraltext 1 (3 r + 2 r 2 sin dr ) d = integraltext 2 ([ 3 r 2 2 + 2 r 3 3 sin ] 1 ) d = integraltext 2 ( 3 2 + 2 3 sin ) d = 3 (1 mark) (b) We have z = 0. (1 mark) The circle is parametrised by...
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quizbmarkscheme123 - Math2061 Vector Calculus Quiz Version...

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