(a)The vectors A and B are given by:
A=2i +3j +7k
B=-i + 6j -5k
Calculate:-
(i)A×B (ii)A•B (iii) Angle between A and B. (9 marks)
(b)Prove that for any vector function A, the divergence of its curl is zero as in the equation below,
Show that[??•(??×A)]=0 (4 marks)
(c)(i)State the principle of conservation of angular momentum.(1 mark)
(ii)If a particle of mass (m) at a point, whose position vector is (r) moves in a force field F, show that the torque produced is the rate of change in angular momentum.(4 marks)
(d)The depth (h) of a valley in metres is given by;
h(x,y) =3 x2 + 2y2 -50x + xy +20y +300
where y is the distance in meters north and x is the distance in meters east of a tower
Determine:
(i)Co-ordinates of the lowest point on the valley from the tower.
(ii)The depth of the valley . (7 marks)
(e) A body has an initial angular velocity of 3 rad/sec and a constant angular acceleration of 2 rad/sec2. Calculate the
(i)Angular displacement after 3 seconds.
(ii)Angular velocity at t= 3 seconds (5 marks)
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