Three vectors are defined by position vectors defined as ā = 2i+ j-3k, b = -3i+2j- 4k and č = xi+ yj– zk , where x, y, z represent the last three digits of your index number. Calculate the:- i) a• (bx ck a ii)

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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last three digits of index number - 0,7,1
QUESTION 3.
a)
Three vectors are defined by position vectors defined as
ā = 2i+ j- 3k, b= -3i+2j- 4k and č = xi+ yj- zk , where x, y, z
||
represent the last three digits of your index number. Calculate the:-
i)
a• (bx c)
(ix ck a
ii)
b)
Find the curl of the vector field, CurlIF, if F= Ax'zi- By 2 j+ Cx z*k,
where the coefficients A, B, C, are the last three digits of
your index number.
c)
A conservative vector field is given as F = 6xe'i + (3x²e" – 10yz')j-15y zk.
Find the potential function f
(4– x² – y³ )
Evaluate the double integral JJ 2M+3N+2P
d)
dA
where coefficients M, N, P are the last three digits of
your index number and C is
positively oriented region bounded by the semi circles with radii ; = 1, r, = 2
centered at the origin and lying in the first and second quadrants of the
Cartesian plane.
Transcribed Image Text:QUESTION 3. a) Three vectors are defined by position vectors defined as ā = 2i+ j- 3k, b= -3i+2j- 4k and č = xi+ yj- zk , where x, y, z || represent the last three digits of your index number. Calculate the:- i) a• (bx c) (ix ck a ii) b) Find the curl of the vector field, CurlIF, if F= Ax'zi- By 2 j+ Cx z*k, where the coefficients A, B, C, are the last three digits of your index number. c) A conservative vector field is given as F = 6xe'i + (3x²e" – 10yz')j-15y zk. Find the potential function f (4– x² – y³ ) Evaluate the double integral JJ 2M+3N+2P d) dA where coefficients M, N, P are the last three digits of your index number and C is positively oriented region bounded by the semi circles with radii ; = 1, r, = 2 centered at the origin and lying in the first and second quadrants of the Cartesian plane.
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